{"id":3838,"date":"2006-12-20T12:21:00","date_gmt":"2006-12-20T03:21:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3838"},"modified":"2021-08-12T12:01:30","modified_gmt":"2021-08-12T03:01:30","slug":"%e1%84%89%e1%85%a5%e1%86%ab%e1%84%92%e1%85%a7%e1%86%bc%e1%84%83%e1%85%a2%e1%84%89%e1%85%ae%e1%84%8c%e1%85%b5%e1%86%af%e1%84%86%e1%85%ae%e1%86%ab%e1%84%87%e1%85%a1%e1%86%bc","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2006\/12\/20\/%e1%84%89%e1%85%a5%e1%86%ab%e1%84%92%e1%85%a7%e1%86%bc%e1%84%83%e1%85%a2%e1%84%89%e1%85%ae%e1%84%8c%e1%85%b5%e1%86%af%e1%84%86%e1%85%ae%e1%86%ab%e1%84%87%e1%85%a1%e1%86%bc\/","title":{"rendered":"\u1109\u1165\u11ab\u1112\u1167\u11bc\u1103\u1162\u1109\u116e\u110c\u1175\u11af\u1106\u116e\u11ab\u1107\u1161\u11bc"},"content":{"rendered":"

\uc9c8\ubb38\uc740 Q: \ub97c \ub9d0\uba38\ub9ac\uc5d0 \ubd99\uc774\uace0 \uc368 \uc8fc\uace0, \ub2f5\uae00\uc740 A:\ub97c \ub9d0\uba38\ub9ac\uc5d0 \ubd99\uc774\uba74 \uc88b\uaca0\ub124\uc694. \ub2f5\uae00\uc740 \ud55c\uc904 \ube44\uc6b0\uace0 \uc0c8 \uc904\uc5d0 \uc2dc\uc791\ud558\uba70 A: \uc55e\uc5d0\ub294 \uacf5\ubc31\uc744 \ub123\uc5b4\uc11c \ub4e4\uc5ec\uc4f0\uae30\uac00 \ub418\uac8c \ud574\uc8fc\uc138\uc694. \ub610 \uae00 \ub9c8\uc9c0\ub9c9\uc5d0\ub294 \uc790\uc2e0\uc758 \uc774\ub984\uc744 \ubd99\uc5ec\uc8fc\uc138\uc694. <\/p>\n

\uae00\uc744 \uc4f0\ub294 \ubc29\ubc95\uc740 \uba54\ub274 \uac00\uc6b4\ub370 ”’\uace0\uce58\uae30”’\ub97c \ub204\ub974\uace0 \ub098\ud0c0\ub098\ub294 \ud3b8\uc9d1\ucc3d\uc5d0 \uc544\ub798\uc640 \uac19\uc774 \uc785\ub825\ud569\ub2c8\ub2e4. \uc911\uac04 \uc911\uac04\uc5d0 \ubbf8\ub9ac\ubcf4\uae30\ub97c \ud574\ub3c4 \ub418\uace0\uc694, \ub9c8\uc9c0\ub9c9\uc5d0\ub294 \uaf2d \uc800\uc7a5\uc744 \ub20c\ub7ec\uc11c \uc368\ub193\uc740 \uae00\uc774 \uc5c6\uc5b4\uc9c0\uc9c0 \uc54a\ub3c4\ub85d \ud569\ub2c8\ub2e4. <\/p>\n

”’\uae00\uc740 \ucd5c\uadfc \uac83\uc744 \uac00\uc7a5 \uc704\uc5d0 \uc501\ub2c8\ub2e4.”’ <\/p>\n

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Q : \ub2f5\ubcc0 \uc815\ub9d0 \uac10\uc0ac\ud569\ub2c8\ub2e4^^ \uc870\uae08\ub9cc \ub354 \uc5ec\ucb64\ubcfc\uaed8\uc694….\uadf8\ub7fc jordan form\uc774 \uac19\uc73c\uba74 similar\ud55c \uac74\uac00\uc694???? \uadf8\ub9ac\uad6c \uc81c\uac00 \uac1c\ub150\uc774 \uc798 \uc548\uc7a1\ud600\uc11c \uadf8\ub7ec\ub294\ub370\uc694, jordan form\uc744 \ud558\ub294 \uc774\uc720\uac00 \ucda9\ubd84\ud55c eig,vec\uc774 \uc5c6\ub294 \uacbd\uc6b0 \uc989 \ub300\uac01\ud654\uac00 \uc548\ub420 \ub54c \ub300\uac01\ud654 \uc2dc\ud0a4\ub824\uace0 \ud558\ub294 \uac70 \ub9de\uc8e0????(2005.11.21.\uae40\uc740\ud76c) <\/p>\n

A : A\uc640 B\uc758 Jordan form\uc774 \uac19\ub2e4\uba74 \\[ P^-^1 A P = Q^-^1 B Q \\] \uc774\ub807\uac8c \uc4f8 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc2dd\uc744 \uc801\uc808\ud788 \ubcc0\ud615\ud574\uc8fc\uba74 \\[ Q P^-^1 A P Q^-^1 = B \\] \uac00 \ub429\ub2c8\ub2e4. \\[ P Q^-^1 = R \\] \uc774\ub77c\uace0 \uce58\ud658\ud574\uc8fc\uba74 \\[ R^-^1 A R = B \\] \ub77c\uace0 \ud45c\ud604 \ub418\ubbc0\ub85c A\uc640 B\ub294 Similar\ub77c\uace0 \ubcfc \uc218 \uc788\uc2b5\ub2c8\ub2e4. Jordan form\uc740 \ub9d0\uc500\ud558\uc2e0\ub300\ub85c \ub300\uac01\ud654\uac00 \ub418\uc9c8 \uc54a\uc744 \ub54c \ucc28\uc120\ucc45\uc73c\ub85c \uc4f0\uc785\ub2c8\ub2e4. \ub9de\ub098\uc694 -_-; (2005.11.21. \uc870\ube44\ud638) \ub9de\uc544\uc694. – \uae40\uc601\uc6b1 <\/p>\n

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Q : similar\uc5d0 \ub300\ud574 \uad81\uae08\ud55c \uac83\uc774 \uc788\ub294\ub370\uc694, \ub450 matrix\uac00 similar\ud560 \uacbd\uc6b0\uc5d0\ub294 \uac19\uc740 eigenvalue set\uc744 \uac16\uace0 \uc774 \ub9d0\uc740 \uac19\uc740 characteristic polynomial\uc744 \uac16\ub294\ub2e4\uc640 \ub3d9\uce58\uc774\ub2e4\ub77c\uace0 \ub178\ud2b8\uc5d0 \ud544\uae30\ub97c \ud588\ub294\ub370\uc694(\uac15\uc758\ub85d\uc5d0\ub3c4 \uadf8\ub807\uac8c \ub098\uc640\uc788\uc5b4\uc694…)….\uc774\uac8c \uc11c\ub85c \ud544\uc694\ucda9\ubd84\uc778\uac00\uc694? similar\ud560 \uacbd\uc6b0\uc5d0 \uc800 \uc131\uc9c8\uc774 \uc131\ub9bd\ud558\ub294\ub370 \uc5ed\uc73c\ub85c characteristic polynomial\uc774 \uac19\uc73c\uba74 similar\ub77c\uace0 \ub9d0\ud560 \uc218 \uc788\ub098\uc694?? \uad81\uae08\ud569\ub2c8\ub2e4..\uc54c\ub824\uc8fc\uc138\uc694…^^(2005.11.21.\uae40\uc740\ud76c) <\/p>\n

A: \ud760…\uc81c\uac00 \ub2f5\ubcc0\uc744 \ud574\ub3c4 \ub418\ub294\uc9c0\ub294 \uc798 \ubaa8\ub974\uaca0\uc9c0\ub9cc..^^ \uc6b0\uc120 \ub450\ud589\ub82c A,B\uc758 characteristic polynomial\uc774 \uac19\ub2e4\uace0 \ud574\uc11c \ub450 \ud589\ub82c\uc774 similar \ud55c \uac83\uc740 \uc544\ub2d9\ub2c8\ub2e4. \ub3d9\uce58 \uc870\uac74\uc744 \uc815\ud655\ud788 \ub9d0\ud558\uc790\uba74 <\/p>\n

A is similar to B iff A and B have the same Jordan form iff nullity(A-sI)^j=nullity(B-sI)^j is true for all eigenvalue s. <\/p>\n

\uc785\ub2c8\ub2e4. \uc544\ub9c8\ub3c4 \uac15\uc758\ub85d\uc758 \ub3d9\uce58 \uc870\uac74 eigen value set\uc774 \uac19\ub2e4\ub294 \ub9d0\uc758 \uc758\ubbf8\ub294 nuillity(A-sI)^j=nuillity(B-sI)^j is true for all eigen value s \uc5d0\uc11c \ub098\uc628 \ub9d0 \uc77c \uac83\uc785\ub2c8\ub2e4. \uc774\ub294 \uc219\uc81c \ubb38\uc81c 4\ubc88\uc5d0\uc11c\ub3c4 \ud655\uc778 \ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc989 char polyn \uc774 (s-1)^3 \uc774\uc9c0\ub9cc \uc11c\ub85c similar \ud558\uc9c0 \uc54a\uc740 \ud589\ub82c\uc774 \uc874\uc7ac\ud569\ub2c8\ub2e4. \uac00\ub2a5\ud55c minimal polyn \uc5d0 \ub530\ub77c Jordan block\ub97c \ub098\ub204\uc5b4 \ubcf4\uc138\uc694. \ud55c\ud3b8 characteristic polyn \uc774 muliple root\ub97c \uac00\uc9c0\uc9c0 \uc54a\ub294 \uacbd\uc6b0\uc5d0\ub294 characteristic polyn \uc774 \uac19\ub2e4\uba74 \ub450 \ud589\ub82c\uc740 similar \ud558\ub2e4\uace0 \ub9d0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc65c\ub0d0\ud558\uba74 char polyn \uc758 \uadfc\uc774 \ubaa8\ub450 \uc11c\ub85c \ub2e4\ub974\ub2e4\uba74(= \ubaa8\ub450 \uc11c\ub85c \ub2e4\ub978 eigenvalue\ub97c \uac00\uc9d0) \uc774\ub294 \ub300\uac01\ud654\uac00 \uac00\ub2a5\ud558\uae30 \ub54c\ubb38\uc774\uc8e0. \uc774\ub294 \uc219\uc81c 2\ubc88\uc5d0\uc11c \ud655\uc778 \ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.(2005.11.21.\uc2e0\uc601\uc2dd) \uc88b\uc2b5\ub2c8\ub2e4. – \uae40\uc601\uc6b1 <\/p>\n

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Q : \uc219\uc81c \ubb38\uc81c 5\ubc88\uc744 \ud480\ub2e4\uac00 \uad81\uae08\ud55c \uc810\uc774 \uc0dd\uacbc\uc2b5\ub2c8\ub2e4. Calely-Hamilton \uc815\ub9ac\uc5d0 \uc758\ud558\uc5ec characteristic polynomial\uc758 \uc2dd\uc5d0 \ud589\ub82c A\ub97c \ub300\uc785\ud558\uba74 0\uc778 \uac83\uc744 \uc218\uc5c5 \uc2dc\uac04\uc5d0 \ubc30\uc6b4\uc801\uc774 \uc788\uc5c8\ub294\ub370, \uc5ed(?)\ub3c4 \uc131\ub9bd\ud558\ub294 \uc9c0\uac00 \uad81\uae08\ud569\ub2c8\ub2e4. \uc989, \ud589\ub82c A \uc5d0 \uad00\ud55c polynomial equation\uc774 0 \uc774\ub77c\uba74 A \ub300\uc2e0 s \ub97c, I \ub300\uc2e0 1\uc744 \ub300\uc785\ud55c \uac83\uc744 \uc774\uc6a9\ud558\uc5ec characteric polynomial\uc744 \uad6c\ud560 \uc218\uac00 \uc788\ub294 \uc9c0\uac00 \uad81\uae08\ud569\ub2c8\ub2e4. \uc774 \ubb38\uc81c\uc5d0\uc11c\uc758 \ud480\uc774\ub294 \uc815\ud655\ud55c characteristic polynomial\uc740 \uc54c \uc218 \uc5c6\uc9c0\ub9cc minimal polynomial \uc774 \ub420 \uc218 \uc788\ub294 \uac83\uc740 \uad6c\ud560 \uc218 \uc788\ub294 \uac83 \uac19\uc740\ub370 \uadf8\ub807\ub2e4\uba74 characteristic polynomial\uc740 \uc774 minimal polynomial\uc5d0 i, j \uc2b9\uc744 \ud55c form \uc774\ub77c\uace0 \ub9d0\ud560 \uc218 \uc788\ub294 \uac83\uc785\ub2c8\uae4c? (2005.11.20. \uc2e0\uc601\uc2dd) <\/p>\n

A: \ud589\ub82c\uc744 \ubaa8\ub974\uba74\uc11c \ud589\ub82c\uc774 \ub9cc\uc871\ud558\ub294 \ub2e4\ud56d\uc2dd \ud558\ub098\ub9cc \uc54c\uace0\uc11c \uadf8 characteristic polyn\uc744 \uad6c\ud560 \uc218 \uc5c6\uc5b4\uc694.\uc6b0\ub9ac\uac00 \uc54c \uc218 \uc788\ub294 \uac83\uc740 \uadf8 \ub2e4\ud56d\uc2dd\uc758 \uc778\uc218 \uac00\uc6b4\ub370 \uc774 \ud589\ub82c\uc758 minimal polyn\uc774 \uc788\ub2e4\ub294 \uc0ac\uc2e4\ub9cc \uc54c \uc218 \uc788\uc5b4\uc694. A\uc758 size\ub97c \uc54c\uace0 \uc788\uc5b4\ub3c4 \uc544\ub9c8 ch. polyn.\uc740 \uc54c \uc218 \uc5c6\uc744 \uac70\uc608\uc694. \uadf8\ub9ac\uace0 ch. polyn.\uacfc minimal polyn.\uc758 \uad00\uacc4\ub294 \uac01 1\ucc28 \uc778\uc218\ub294 \ubaa8\ub450 \uc77c\uce58\ud558\ub294\ub370 \uadf8 \ucc28\uc218\ub9cc\uc774 \ucc28\uc774\ub09c\ub2e4\ub294 \uad00\uacc4\ub97c \uac00\uc9c0\uace0 \uc788\uc9c0\uc694. – \uae40\uc601\uc6b1 <\/p>\n

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Q : QR decomposition\uc5d0 \ub300\ud574\uc11c \uad81\uae08\ud55c \uc810\uc774 \uc788\uc2b5\ub2c8\ub2e4. \ud558\ub098\uc758 Matrix\ub97c QR decomposition\uc5d0 \uc758\ud574 \ubd84\ub9ac\ud560 \uacbd\uc6b0, \ud558\ub098\uc758 \uacb0\uacfc\ub9cc \ub098\ud0c0\ub0a0\uae4c\uc694? \uc989 A=QR\uc744 \ub9cc\uc871\ud558\ub294 QR\uc740 \ud558\ub098\ub9cc \ub420 \uc218 \uc788\ub294\uc9c0 \uad81\uae08\ud569\ub2c8\ub2e4. \ub9cc\uc57d \uc5ec\ub7ec\uac1c\uc758 QR decomposition\uc774 \uac00\ub2a5\ud558\ub2e4\uba74, Gram-Schmidt process\uac00 \uc544\ub2cc \ub2e4\ub978 process\uac00 \ud544\uc694\ud560 \uac83 \uac19\uc740\ub370\uc694, \ucc38\uace0 \uc11c\uc801\uc744 \ucc3e\uc544\ubd24\ub294\ub370 \uc798 \ubabb\ucc3e\uaca0\uc2b5\ub2c8\ub2e4. \uc758\ub3c4\ud558\ub294 \ubc14\ub294 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4. A, B Matrix\uac00 \uc788\uace0, \uc774\ub97c \uac01\uac01 QR decomposition\ud558\ub3c4\ub85d \ud558\ub294\ub370, A\uc5d0\uc11c \uc0ac\uc6a9\ud588\ub358 basis(v1, v2, v3)\ub97c B\uc5d0\uc11c \ub611\uac19\uc774 \uc801\uc6a9\ud558\ub824\uace0 \ud569\ub2c8\ub2e4. \uadf8\ub7f0\ub370 Gram Schmidt \ubc29\uc2dd\uc5d0\uc11c\ub294 u1 = v1\uc73c\ub85c \uc2dc\uc791\ud558\uae30 \ub54c\ubb38\uc5d0, u1 = a1v1 + a2v2 + a3v3\ub85c \uc120\ud615\uacb0\ud569\ub418\uc5c8\uc744 \uacbd\uc6b0\ub97c \ud3ec\ud568\ud558\uc9c0 \uc54a\ub294 \uac83 \uac19\uc2b5\ub2c8\ub2e4. \uc544\ub798 orthonormal basis\uc5d0 \ub300\ud55c \uc9c8\ubb38\uc758 \uc5f0\uc7a5\uc120\uc778 \uac83 \uac19\uc2b5\ub2c8\ub2e4\ub9cc. \uc544\ubb34\ucabc\ub85d \ub2f5\ubcc0 \uac10\uc0ac\ud569\ub2c8\ub2e4.(2005.10.05 \uae40\ud615\ub144) <\/p>\n

A: \uc804 \uc218\uac15\uc0dd\uc774\uc9c0\ub9cc \uac10\ud788 \ub2f5\ubcc0\uc744 \ud558\uc790\uba74…\uc6b0\uc120 Orthonormal basis\ub294 \uc77c\ubc18\uc801\uc73c\ub85c \ubb34\ud55c\ud788 \ub9ce\uc73c\ub2c8 QR Decomposition\uc758 \uacb0\uacfc\ub3c4 \ubb34\ud55c\ud788 \ub9ce\uc740 \uacb0\uacfc\uac00 \uc788\uaca0\uc8e0. \uadf8\ub807\ub2e4\uace0\ud574\uc11c \ub2e4\ub978 Process \uac00 \ud544\uc694\ud560 \uc774\uc720\ub294 \uc5c6\uc2b5\ub2c8\ub2e4. Gram-Schmidt process \uc790\uccb4\ub85c \uc774\ubbf8 \ubb34\ud55c\ud788 \ub9ce\uc740 Orthonormal basis\ub97c \ub9cc\ub4e4\uc218 \uc788\uc73c\ub2c8\uae4c\uc694. \uadf8\ub9ac\uace0 \ub450\ubc88\uc9f8 \uc9c8\ubb38\uc744 \ubcf4\ub2c8 QR Decomposition\uc5d0 \ub300\ud574\uc11c \uc81c\ub300\ub85c \uc774\ud574\ud558\uc9c0 \ubabb\ud558\uc2e0 \ubd80\ubd84\uc774 \uc788\ub294 \uac83 \uac19\uc740\ub370\uc694. \uc9c8\ubb38\uc5d0\uc11c \uc4f0\uc2e0 \ud589\ub82c A, B \uc790\uccb4\uac00 basis \ub97c column vector \ub85c \ub098\uc5f4\ud558\uc5ec \uc774\ub8e8\uc5b4\uc9c4 \ud589\ub82c\uc774\uae30 \ub54c\ubb38\uc5d0, ‘A\uc5d0\uc11c \uc0ac\uc6a9\ud55c basis \ub97c B\uc5d0 \ub611\uac19\uc774 \uc801\uc6a9\ud55c\ub2e4’\ub294 \ub9d0\uc740 ‘A\uc640 B\uac00 \uc644\uc804\ud788 \uac19\uc740 \ud589\ub82c’\uc774\ub77c\ub294 \ubcc4\uc758\ubbf8\uc5c6\ub294 \ub9d0\uacfc \uac19\uc2b5\ub2c8\ub2e4. <\/p>\n

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Q : \ud55c\uac00\uc9c0 \ub354 \uc5ec\ucb64\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. Least Square Method\uc758 \uacbd\uc6b0, basis\uc5d0 projection\ud558\uc5ec \ucd5c\uc18c \uac70\ub9ac\uac12\uc744 \uad6c\ud558\ub294 \uac8c \ub418\ub294\ub370\uc694, 2-Dimension\uc5d0\uc11c best fitting\uc744 \uc704\ud558\uc5ec projection\ud558\uc600\uc744 \uacbd\uc6b0 \uc2e4\uc81c data\uc640 fitting line \uc0ac\uc774\uc758 y\ucd95 \ucc28\uc774 \uac12\uc744 \uc81c\uacf1\ud558\uc5ec \uad6c\ud558\ub294 \uac83 \uac19\uc2b5\ub2c8\ub2e4. \uadf8\ub7f0\ub370 best fitting\uc774\ub77c\ub294 \uce21\uba74\uc5d0\uc11c \ubcf4\uc790\uba74, y\ucd95\uacfc\uc758 \uac70\ub9ac\uac00 \uc544\ub2c8\ub77c, \uc2e4\uc81c data 2\ucc28\uc6d0 \uc810\uacfc fitting line \uc0ac\uc774\uc758 \uac70\ub9ac(not y\ucd95 \uac70\ub9ac)\ub97c \ucd5c\uc18c\ub85c \ud574\uc57c \ud558\ub294 \uac83\uc774 \uc544\ub2d0\uae4c\uc694? \uc989, fitting line (ax + by + c = 0 : a, b, c\ub294 \ubbf8\uc9c0\uc218)\uacfc data point (Xn, Yn : n = 1 ~ N)\uac04\uc758 \uac70\ub9ac\ub97c summation\ud574\uc57c \ud560\ud150\ub370, \uadf8\ub7ac\uc744 \uacbd\uc6b0, least square method\uc640\ub294 \ub2e4\ub978 \uc2dd\uc774 \ub418\uc9c0 \uc54a\uc744\uae4c\uc694? \uadf8\ub807\ub2e4\uba74 \uc2e4\uc81c \uc810\uacfc \uc120\uc0ac\uc774\uc758 \uac70\ub9ac\ub97c \ucd5c\uc18c\ub85c \ud558\ub294 \ubc29\uc2dd\uc73c\ub85c best fitting\ud558\ub294 \ubc29\ubc95\uc740 \ubb34\uc5c7\uc774 \uc788\uc744\uae4c\uc694? (2005.09.20 \uae40\ud615\ub144) <\/p>\n

A: best fitting\uc740 \uac01 \ubcc0\uc218\uac12 t\uc5d0\uc11c\uc758 \ud568\uc218\uac12\uc758 \ucc28\uac00 \ucd5c\uc18c\uc758 \uc624\ucc28\ub97c \uac00\uc9c0\uae30\ub97c \ubc14\ub78d\ub2c8\ub2e4.(\uc774\uac74 \ud1b5\uacc4\uc758 \ubb38\uc81c\uc774\uc9c0\uc694.) \uadf8 \uacbd\uc6b0 \uc6b0\ub9ac\uac00 \ud55c \ubc29\ubc95(Gauss\uc758 \ubc29\ubc95)\uc774 \uc633\uc2b5\ub2c8\ub2e4. \ud615\ub144\uad70\uc774 \uc774\uc57c\uae30\ud558\ub294 fitting\uc740 \ud568\uc218\uac12\uc758 \uc624\ucc28\ub97c \uc904\uc774\ub294 \uac83\uc774 \uc544\ub2c8\ub77c \uadf8\ub798\ud504\uc758 \uc810\uc758 \uc704\uce58\uc5d0 \ub300\ud55c fitting\uc774\uace0 \uc774\uac83\uc740 \ub2e4\ub978 \ubb38\uc81c\uc785\ub2c8\ub2e4. \uc774 \uacbd\uc6b0\ub294 \uc810-valued\uc778 \ud568\uc218\ub85c \uc0dd\uac01\ud558\uba74 \ub610 \uac19\uc544\uc9d1\ub2c8\ub2e4. \uc989 (x(t), y(t))\ub77c\ub294 \ud568\uc218\ub97c \uac01 t \ub9c8\ub2e4 \uac12\uc744 \uc54c \ub54c \uc774 \ud568\uc218\uac12\uc774 \uac00\uc7a5 \uc624\ucc28\uac00 \uc791\uac8c \ub9cc\ub4dc\ub294 \uac83\uc774 \ub420 \uac81\ub2c8\ub2e4. – \uae40\uc601\uc6b1 <\/p>\n

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Q : \uc624\ub298 \uc218\uc5c5\uc911\uc5d0 orthonormal basis\ub97c \uad6c\ud558\ub294 process\uac00 \uc788\uc5c8\ub294\ub370\uc694, {v1, v2 , … , vn}\uc5d0\uc11c v1\ubd80\ud130 \uc2dc\uc791\ud558\uc5ec v2, v3… \ub97c \ucc28\ub840\ub85c \uc720\ub3c4\ud588\uc2b5\ub2c8\ub2e4. \uadf8\ub7f0\ub370 \ub9cc\uc57d v2\ubd80\ud130 \uc2dc\uc791\ud55c orthonormal basis\ub97c \uad6c\ud55c\ub2e4\uba74 \ucc98\uc74c\uc5d0 \uad6c\ud55c orthonormal basis\uc640 \ub2e4\ub978 \ud615\ud0dc\uc758 basis\uac00 \uad6c\uc131\ub420 \uac83 \uac19\uc2b5\ub2c8\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c v3\uc5d0\uc11c \uc2dc\uc791\ud55c basis\ub85c \ubd80\ud130 v1, v2, v4…\ub4f1\uc744 \ucd94\ucd9c\ud560 \uc218 \uc788\uad6c\uc694. \uadf8\ub807\ub2e4\uba74, \ud558\ub098\uc758 vector\ub97c n\uac1c\uc758 orthonormal basis set\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4\ub294 \uac83\uc778\ub370, \uc774\ub7ec\ud55c n\uac1c\uc758 basis set\ub4e4\uac04\uc758 \uad00\uacc4\ub294 \ubb34\uc5c7\uc77c\uae4c\uc694? v1\ubd80\ud130 \uc2dc\uc791\ud574\uc57c \ud55c\ub2e4\ub294 \uaddc\uce59\uc774 \uc5c6\ub2e4\uba74 basis\uc758 \uacc4\uc218\ub4e4\uac04\uc758 \uad00\uacc4\ub97c \uc0b4\ud3b4\ubcf4\ub294 \uacfc\uc815\uc5d0\uc11c\ub3c4 \ubb38\uc81c\uac00 \ubc1c\uc0dd\ud558\uc9c0 \uc54a\uc744\uae4c\uc694? (2005.09.20 \uae40\ud615\ub144) <\/p>\n

A: orthonormal basis\ub294 \ubb34\ud55c\ud788 \ub9ce\uc2b5\ub2c8\ub2e4. \uc774 \uac00\uc6b4\ub370 \uc8fc\uc5b4\uc9c4 basis\uc640 (\uc21c\uc11c\uae4c\uc9c0\ub3c4) \uc798 \ub9de\ub294 \uac83\uc744 \ud558\ub098 \ucc3e\ub294 \ubc29\ubc95\uc77c \ubfd0\uc785\ub2c8\ub2e4. \uc774 \uacbd\uc6b0 \uc21c\ucc28\uc801\uc73c\ub85c \uc6d0\ub798 basis\uc640 \uc0c8 basis\uac00 \uc798 \ub9de\uc544\ub4e4\uc5b4\uac11\ub2c8\ub2e4. \uc989, k\ubc88\uc9f8\uae4c\uc9c0\uc758 basis\uc758 span\uc740 \uc0c8 basis\uc5d0\uc11c\ub3c4 k\ubc88\uc9f8\uae4c\uc9c0\uc758 basis\uc758 span\uacfc \uc77c\uce58\ud569\ub2c8\ub2e4. \uc21c\uc11c\ub97c \ubc14\uafb8\uc5b4\uc11c \ud558\uba74 \uc774\ub7f0 \ub0b4\uc6a9\uc774 \ub2ec\ub77c\uc9c0\uc9c0\ub9cc \uc774 \uc0c8\ub85c\uc6b4 \uc21c\uc11c\uc5d0 \ub300\ud558\uc5ec\ub294 \uadf8\ub300\ub85c \uc798 \ub9de\ub294 \uac83\uc774 \ub098\uc624\uc9c0\uc694. \uc774\ub4e4 \uc0ac\uc774\uc5d0\ub294 \ud2b9\ubcc4\ud55c \uad00\uacc4\ub294 \uc5c6\uc5b4 \ubcf4\uc785\ub2c8\ub2e4. \ubb3c\ub860 v1\uc5d0\uc11c \uc2dc\uc791\ud574\uc57c \ud55c\ub2e4\ub294 \ubc95\uc740 \uc5c6\ub294 \uac83\uc774\uc9c0\uc694. \ud544\uc694\uc5d0 \ub9de\uac8c \uc21c\uc11c\ub3c4 \uc815\ud558\uace0 \ucc3e\uc73c\uba74 \ub429\ub2c8\ub2e4. – \uae40\uc601\uc6b1 <\/p>\n

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Q : \uacf5\ubd80\ud558\ub2e4 \ubcf4\ub2c8 linear,bilinear,multilinear \uc774\ub7f0\uac83\ub4e4\uc774 \ub098\uc624\ub358\ub370\uc694. linear\ud558\ub2e4\ub294 \uac83\uc740 \uc774\ud574\uac00 \uac00\ub294\ub370 \ub098\uba38\uc9c0 \ub450 \uac1c\ub150\uc740 \uc774\ud574\uac00 \uac00\uc9c0 \uc54a\uc2b5\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \uc5b4\ub5a4 \ud568\uc218\ub4e4\uc774 bilinear,multilinear \ud55c\uac83\uc778\uac00\uc694? (2005.08.25 \uc815\ud638) <\/p>\n

A: \uc870\uae08 \uc788\uc73c\uba74 \uacf5\ubd80\ud560 \uac70\uc9c0\ub9cc\uc694 bilinear \ud568\uc218\uc758 \ub300\ud45c\uc801\uc778 \uc608\ub294 \ub0b4\uc801\uc785\ub2c8\ub2e4. $ a ⋅ b $ \ub294 \ub450 \ubca1\ud130\uc758 \uc30d $ (a,b) $ \ub97c \ubcc0\uc218\ub85c \ud558\ub294 \ud568\uc218\uc778\ub370 $ a $ \uc5d0 \ub300\ud558\uc5ec\ub3c4 \uc120\ud615\ud568\uc218\uc774\uace0 $ b $ \uc5d0 \ub300\ud558\uc5ec\ub3c4 \uc120\ud615\ud568\uc218\uc778 \uc30d\uc120\ud615\ud568\uc218(bilinear form)\uc785\ub2c8\ub2e4. \ud55c\ud3b8 \uc14b \uc774\uc0c1\uc758 \ubca1\ud130\uc5d0 \ub300\ud55c multilinear \ud568\uc218\uc758 \uc608\ub85c\ub294 (\ubb3c\ub860 \ub0b4\uc801\uc774 bilinear \uc774\ub2c8\uae4c n=2 \uc778 multilinear \uc774\uc9c0\ub9cc) \ud589\ub82c\uc2dd(determinant)\uac00 \ub300\ud45c\uc801\uc785\ub2c8\ub2e4. 3×3 \ud589\ub82c\uc758 \ud589\ub82c\uc2dd\uc740 \ud589\ubca1\ud130 3\uac1c\uc5d0 \ub300\ud55c \ud568\uc218\ub85c \ubcf4\uba74 \uac01\uac01\uc758 \ubca1\ud130\uc5d0 \ub300\ud558\uc5ec \uc120\ud615\ud568\uc218\uc774\ub2c8\uae4c tri-linear\uc785\ub2c8\ub2e4. \uc774\ub7f0 \uc2dd\uc758 \ud568\uc218\ub294 \uadf8\ub9ac \ub9ce\uc9c0 \uc54a\uc544\uc11c \ubaa8\ub450 \ub9cc\ub4e4 \uc218 \uc788\ub294\ub370 \uc774\ub7f0 \uc774\ub860\uc740 \ub300\uc218\ud559\uc5d0\uc11c \uacf5\ubd80\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \ud2b9\ud788 \ub300\uce6d\uc778 \ud568\uc218\uc640 \uc65c\ub300\uce6d\uc778 \ud568\uc218\uac00 \uc788\uc73c\uba70 \ubaa8\ub4e0 \ub2e4\uc911\uc120\ud615\ud568\uc218\ub294 \uc774\ub7f0 \ub450 \uac00\uc9c0 \ud568\uc218\uc758 \ud569\uc73c\ub85c \ub9cc\ub4e4 \uc218 \uc788\uc5b4\uc694. \uc774\ub7f0\uac83\uc758 \uae30\ubcf8\uc774 \ub300\uce6d\uc2dd\uc774\ub860\uc774\uc9c0\uc694. Like $ a + b $ , $ ab $ \uac00 \ub450 \uc2e4\uc218 \ubcc0\uc218\uc5d0 \ub300\ud55c \ub300\uce6d\uc2dd… \ub4f1\ub4f1. <\/p>\n

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Q:\uc548\ub155\ud558\uc138\uc694. \uc120\ud615\ub300\uc218\uad00\ub828 \uc9c8\ubb38\uc740 \uc544\ub2cc\ub370 \uc9c8\ubb38\ud560\uc218\uc788\ub294\ub370\ub97c \uc5ec\uae30\ubc16\uc5d0 \ubabb\ucc3e\uc544\uc11c \uc5ec\uae30\ub2e4 \uc9c8\ubb38\ud558\uac8c \ub418\uc5c8\uc2b5\ub2c8\ub2e4. \uc5b4\uca0c\uac70\ub098 \uc81c\uac00 \ubb3c\ub9ac\ud559\uacfc \ud559\uc0dd\uc774\uc5b4\uc11c \uc77c\ubc18\uc0c1\ub300\uc131\uc774\ub860\uc5d0 \ub300\ud574 \uad00\uc2ec\uc744 \uac00\uc9c0\uace0 \uc788\ub294\ub370\uc694. \uad00\ub828\uc11c\uc801\uc744 \ucc3e\uc544\ubcf4\ub2c8 \ubbf8\ubd84\uae30\ud558\ud559\uc744 \uc5b4\ub290\uc815\ub3c4 \ubc30\uc6cc\ub193\uace0 \uc2dc\uc791\ud574\uc57c \ub420 \uac83 \uac19\ub354\ub77c\uad6c\uc694. \uadf8\ub798\uc11c \ubbf8\ubd84\uae30\ud558\ud559\uc758 \ub0b4\uc6a9 \uc911\uc5d0 \uc77c\ubc18\uc0c1\ub300\uc131\uc774\ub860\uc5d0 \ud544\uc694\ud55c \ub0b4\uc6a9\ub9cc \uace8\ub77c\uc11c \uc77d\uc5b4\ubcf4\ub824\uace0 \ud558\ub294\ub370\uc694.(\uc81c\uac00 \ub4a4\uc801\ub4a4\uc801 \uac70\ub9ac\ub2e4\ubcf4\ub2c8 tensor,one-forms,christoffel symbols,metric,curvature,riemannian manifolds,covariant differentiation \ub4f1\ub4f1 \uc774\ub7f0 \uc6a9\uc5b4\ub4e4\uc774 \ub098\uc624\ub354\ub77c\uad6c\uc694) \ubbf8\uc801\ubd84\ud559\uacfc \uc120\ud615\ub300\uc218\ub97c \uc218\uac15\ud55c \uc785\ubb38\uc790\uac00 \uc77d\uae30\uc26c\uc6b4 \ubbf8\ubd84\uae30\ud558\ud559 \uc11c\uc801\uc744 \uc870\uae08 \uc54c\ub824\uc8fc\uc138\uc694. \uac10\uc0ac\ud569\ub2c8\ub2e4.(050731) – WhoAmI <\/p>\n

A: \uc6b0\uc120 \uc77c\ubc18\uc0c1\ub300\ub860\uc744 \uacf5\ubd80\ud558\ub824\uba74(\ub098\ub294 \uacf5\ubd80\ud55c \uc801\uc774 \uc5c6\uc9c0\ub9cc) \ubbf8\ubd84\uae30\ud558\ud559 \uc911\uc5d0\uc11c \uc77c\ubd80\ub9cc \uc54c\uba74 \ub418\ub294 \uac83\uc774 \uc544\ub2c8\ub77c, \uc804\ubd80 \ub2e4 \uc54c\uc544\uc57c \ud569\ub2c8\ub2e4. \uadf8\ub9ac\uace0 \ub098\uc11c euclid \uacf5\uac04(\ub0b4\uc801)\uc744 \uae30\ubcf8\uc73c\ub85c \ud55c \ubbf8\ubd84\uae30\ud558\ud559\uc758 \uc774\ub860\uc744 \ubaa8\ub450 Minkowski \uacf5\uac04(\ub0b4\uc801)\uc758 \uc774\uc57c\uae30\ub85c \ubc14\uafbc \uacf5\uac04\uc5d0\uc11c \ubb3c\ub9ac\ud559\uc744 \ud558\ub294 \uac81\ub2c8\ub2e4. \ub530\ub77c\uc11c \uae30\ubcf8 \uac1c\ub150\uc740 tensors, forms, metric, curvature, connection \ub4f1\uc758 \uacc4\uc0b0\uc5d0 \uc775\uc219\ud574\uc57c \ud558\uba70 \ud2b9\ud788 positive definite\ud558\uc9c0 \uc54a\uc740 \ub0b4\uc801\uc744 \ub2e4\ub8e8\ub294\ub370\uc5d0\ub3c4 \uc775\uc219\ud574\uc838\uc57c \ud558\ub2c8\uae4c \ub9ce\uc740 \uacf5\ubd80\uac00 \ud544\uc694\ud558\uc9c0\uc694. <\/p>\n

\uad50\uacfc\uc11c\ub85c\ub294 \uc77c\ubc18\uc801\uc778 \ub9ac\ub9cc\uae30\ud558\ud559\uc758 \uad50\uacfc\uc11c\uc640 \uc0c1\ub300\uc131\uc774\ub860\uc774 \uc801\ud78c semi-riemannian geometry \uad50\uacfc\uc11c \ub4f1\uc774 \uc788\ub294\ub370, \ub9ac\ub9cc\uad50\uacfc\uc11c\uc758 \uc785\ubb38\uc11c\ub294 do Carmo\uc758 Riemannian Geometry, Willmore\uc758 Ri… Geo…, \uace0\uc804\uc73c\ub85c Eisenhart\ub098 Weatherburn\uc758 Riemannian Geometry\uac00 \uc788\uace0\uc694. \ubb3c\ub9ac\ud559\uc5d0\uc11c\ub294 Eddington\uacbd\uc774 \uc4f4 The mathematical theory of relativity \ub4f1\uc774 \uc788\uc5b4\uc694. \ub610 Gockeler\/Schucker\uac00 \uc4f4 Diff. geometry, gauge theories, and gravity\ub3c4 \uc788\uace0\uc694. \uc554\ub9cc\ud574\ub3c4 \uacc4\uc0b0\uc774 \uc911\uc694\ud558\ub2c8\uae4c \uc61b\ub0a0 \ucc45\ub4e4\uc774 \ub354 \uc88b\uc744 \uc218\ub3c4. \ud55c\ud3b8 semi-riemannian \uae30\ud558\ub294 \ub300\ud45c\uc801\uc73c\ub85c \ub0b4 \ubc15\uc0ac\ub17c\ubb38 committee\uc168\ub358 O’neill\uad50\uc218\ub2d8\uc758 Semi-riemannian geometry\uac00 \uc788\uace0\uc694 \uc774 \ubc16\uc5d0 \uac04\ub2e8\ud55c \ucc45\uc73c\ub85c\ub294 Frankel\uc758 \ucc45\uc774 \uc788\uc5b4\uc694(\uc81c\ubaa9?), \ubb3c\ub9ac\ucabd\uc5d0\ub3c4 \ub9ce\uc740\ub370 Ward\uc758 General relativity, \ub098 Hawking\/Ellis\uc758 \ucc45\ub4e4\ub3c4 \uae30\ud558\ud559 \ucc45\uc774\ub77c\uace0 \ubcfc \uc218 \uc788\uc5b4\uc694. <\/p>\n

Q: \ube60\ub974\uace0 \uc790\uc138\ud55c \ub2f5\ubcc0 \uc815\ub9d0 \uac10\uc0ac\ud569\ub2c8\ub2e4. (\u3160\u3160\uac10\ub3d9) \uadf8\ub7f0\ub370 \uc120\ud615\ub300\uc218\uc640 \ubbf8\uc801\ubd84\ud559\ub9cc \ubc30\uc6b0\uba74 \ub9ac\ub9cc\uae30\ud558\ud559\uc744 \ubc30\uc6b0\uae30 \uc704\ud55c \uc900\ube44\uac00 \uc5b4\ub290\uc815\ub3c4 \ub418\uc5c8\ub2e4\uace0 \ubd10\ub3c4 \uad1c\ucc2e\uc740\uac00\uc694? \uccab\ud398\uc774\uc9c0\ubd80\ud130 \ucc98\uc74c\ubcf4\ub294 \uc6a9\uc5b4\ub4e4 (homeomorphism \ub4f1\ub4f1..)\uc774 \ub098\uc624\ub294\ub370,, \ubaa8\ub974\ub294 \uc6a9\uc5b4\ub4e4\uc740 \ub2e4\ub978 \ucc45\uc744 \ucc38\uace0\ud574\uac00\uba74\uc11c \ub9ac\ub9cc\uae30\ud558\ud559 \uad50\uacfc\uc11c\ub97c \uc77d\uc5b4\ub098\uac00\ub3c4 \ud070 \ubb34\ub9ac\uac00 \uc5c6\uc744\uae4c\uc694? <\/p>\n

A: \uc6b0\uc120 \uc704\uc0c1\uc218\ud559\uc758 \uae30\ubcf8\uc744 \uc54c\uc544\uc57c \ub429\ub2c8\ub2e4. \ubb3c\ub860 \ucc98\uc74c\uc5d0\ub294 \uc120\ud615\ub300\uc218, \ud574\uc11d\ud559\uc774\uba74 \ucda9\ubd84\ud574 \ubcf4\uc774\uc9c0\ub9cc \ubb38\uc81c\ub294 \ub9ac\ub9cc\uae30\ud558\uc5d0\uc11c \ub2e4\ub8e8\ub294 \ubaa8\ub4e0 \ub0b4\uc6a9\uc758 \ud3ec\uc778\ud2b8\ub294 \uc5b4\ub5bb\uac8c \ubbf8\ubd84\uae30\ud558\uc801 \uc591(quantity)\ub85c\ubd80\ud130 \uc704\uc0c1\uc801\uc778 \uc591\uc744 \uad6c\ud574\ub0b4\ub294\uac00 \ud558\ub294 \uc774\uc57c\uae30\uc5ec\uc11c \ub300\uc218\uc704\uc0c1\uc744 \uc870\uae08(homeomorphism, fundamental group, homology)\uc740 \uc54c\uc544\uc57c \ud558\uace0, \ub610 \ub9ce\uc740 \ubd80\ubd84\uc5d0\uc11c \uc0ac\uc0c1\uc758 \uc5f0\uc18d\uc131\uacfc \ubbf8\ubd84\uac00\ub2a5\uc131\uc774 \uc911\uc694\ud558\uac8c \ubd80\uac01\ub418\ubbc0\ub85c \ud574\uc11d\ud559 \ubcf4\ub2e4 \uc870\uae08 \ub354 \uae4a\uc740 general topology \uadfc\ucc98\uc758 \uc774\uc57c\uae30\ub3c4 \ub3c4\uc6c0\uc774 \ub9ce\uc774 \ub429\ub2c8\ub2e4.(metric space \uc815\ub3c4\ub85c\ub3c4 \ub420\uac70\uc608\uc694.) \uacf5\ubd80\ud574 \ub098\uac00\uba74\uc11c \uac19\uc774 \uacf5\ubd80\ud560 \uc218 \uc788\uc744\uac70\uc608\uc694. <\/p>\n

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Q : vector space \uc5d0\uc11c field\uc5d0 \ub300\ud55c \uc9c8\ubb38\uc785\ub2c8\ub2e4. \uac04\ub2e8\ud788 R^n \uc744 \uc0dd\uac01\ud560\ub54c \uc774 vector space\uac00 \uc815\uc758\ub41c \ud544\ub4dc\uac00 \ub2e4\ub97c\uacbd\uc6b0 dimenstion\uc774\ub098 \uc5b4\ub5a4 \ud2b9\uc9d5\ub4e4\uc774 \ub2e4\ub97c\uc9c0 \uad81\uae08\ud569\ub2c8\ub2e4. \uc608\ub97c\ub4e4\uc5b4 U\ub294 R\uc704\uc5d0\uc11c \uc815\uc758\ub41c space\uc774\uace0 W\ub294 Z\uc704\uc5d0\uc11c \uc815\uc758\ub41c \ud544\ub4dc\uc77c\ub54c \uc5b4\ub5a4 \ucc28\uc774\uc810\uc774 \uc874\uc7ac\ud558\ub294\uac00\uc694?(2005.07.02 \uc815\ud638) <\/p>\n

A: \uc608\ub97c \ub4e4\uc5b4 \ubd05\ub2c8\ub2e4. <\/p>\n\n\n\n\n\n<\/colgroup>\n\n\n\n\n\n\n\n\n\n
vector space<\/td>\nscalar field<\/td>\ndimension<\/td>\n<\/tr>\n
$ \\mathbb{R} $ (\uc2e4\uc218)<\/td>\n$ \\mathbb{R} $<\/td>\n1<\/td>\n<\/tr>\n
$ \\mathbb{R} $<\/td>\n$ \\mathbb{Q} $ (\uc720\ub9ac\uc218)<\/td>\n\ubb34\ud55c\ucc28\uc6d0<\/td>\n<\/tr>\n
$ \\mathbb{C} $ (\ubcf5\uc18c\uc218)<\/td>\n$ \\mathbb{C} $<\/td>\n1<\/td>\n<\/tr>\n
$ \\mathbb{C} $<\/td>\n$ \\mathbb{R} $<\/td>\n2<\/td>\n<\/tr>\n
$ \\mathbb{C}^n $<\/td>\n$ \\mathbb{C} $<\/td>\n$ n $<\/td>\n<\/tr>\n
$ \\mathbb{C}^n $<\/td>\n$ \\mathbb{R} $<\/td>\n$ 2n $<\/td>\n<\/tr>\n
 <\/td>\n <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\uc815\uc218\uc758 \uad70 $ \\mathbb{Z} $ \ub294 \uccb4(field)\uac00 \uc544\ub2c8\ubbc0\ub85c \ubca1\ud130\uacf5\uac04\uc758 scalar\uac00 \ub420 \uc218 \uc5c6\uc5b4\uc694. \uc774\ub807\uac8c \ub367\uc148, \ube84\uc148, \uacf1\uc148\ub9cc\uc744 \ud560 \uc218 \uc788\ub294 \uac83(\ub098\ub217\uc148 \uc5c6\uc774)\uc744 \ud658(ring)\uc774\ub77c \ud558\uace0\uc694, ring\uc744 scalar\ub85c \ud558\ub294 \ub9c8\uce58 \ubca1\ud130\uacf5\uac04 \uac19\uc740 \uac83\uc744 \uc774 ring \uc704\uc5d0\uc11c \uc815\uc758\ub41c \uac00\uad70(\u52a0\u7fa4,module)\uc774\ub77c\uace0 \ud558\uc9c0\uc694. \ubb3c\ub860 module\ub3c4 \ucc28\uc6d0\uc744 \uc774\uc57c\uae30\ud560 \uc218\ub294 \uc788\uc9c0\ub9cc… <\/p>\n

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Q : \uc624\ub298 \uc2dc\ud5d8\ubb38\uc81c\uc5d0 \ub300\ud55c \uc9c8\ubb38\uc785\ub2c8\ub2e4. 6\ubc88. “R2 \uc5d0\uc11c P1, P2\uac00 y= 1\/2 x \uc640 y = 2 x\ub85c\uc758 \uc815\uc0ac\uc601\uc77c\ub54c Tv = P1v – P2v \uac00 onto \uc784\uc744 \ubcf4\uc774\uc2dc\uc624.”\ub77c\ub294 \ubb38\uc81c\uac00 \uc788\uc5c8\ub294\ub370\uc694. T \ub294 R2\uc5d0\uc11c R2\ub85c\uc758 map \uc774\ub77c\uace0 \uc0dd\uac01\ud558\uace0 \ubb38\uc81c\ub97c \ud480\uc5c8\uc2b5\ub2c8\ub2e4. \uc5ec\uae30\uc11c \uacc4\uc0b0\uc2e4\uc218\ub9cc \ubb34\ud55c\ubc18\ubcf5 \ud558\uc600\uc744\uc9c0\ub3c4 \uc788\uaca0\uc9c0\ub9cc N_T = {(0,a) : a=\uc2a4\uce7c\ub77c}\uc758 \uacf5\uac04\uc774\uba70 \ub530\ub77c\uc11c dim N_T = 1, dim R_T\ub3c4 \ub610\ud55c 1\uc774 \ub418\uc5b4 \uacf5\uc5ed\uc758 \ucc28\uc6d0(=2)\uacfc \uce58\uc5ed\uc758 \ucc28\uc6d0(=1)\uc774 \ub2e4\ub974\ub2e4\ub294 \uacb0\uacfc\uac00 \uacc4\uc18d \ub098\uc654\ub294\ub370\uc694. \uacf5\uc5ed\uc758 \ucc28\uc6d0\uacfc \uce58\uc5ed\uc758 \ucc28\uc6d0\uc774 \ub2e4\ub974\ub2e4\uba74 onto\uac00 \ub420\uc218 \uc5c6\uc9c0 \uc54a\ub098\uc694? \ub610\ud55c P1, P2\ub294 2 x 2 matrix \uc774\uae30\ub54c\ubb38\uc5d0 \uacf5\uc5ed\uc758 \ucc28\uc6d0\uc740 \ub2f9\uc5f0\ud788 2 \uc774\uc9c0 \uc54a\ub098\uc694? \uacb0\uad6d \uc18c\uc2e0\uc744 \uc9c0\ucf1c \ub2f5\uc548\uc9c0\uc5d0\ub294 “T\ub294 onto\uac00 \uc544\ub2c8\ub2e4” \ub77c\uace0 \uc801\uc5c8\ub294\ub370 \u3160\u3160 \ubb34\uc5c7\uc774 \uc798\ubabb\ub418\uc5c8\ub294\uc9c0 \uad81\uae08\ud569\ub2c8\ub2e4. (2005.06.09 \uc2e0\uc601\uc2dd) <\/p>\n

A: \uc6b0\uc120 T\ub294 domain\uacfc codomain\uc774 \uac19\uc740 \uac83\uc774\uc9c0\uc694. (\uc815\uc0ac\uc601\uc758 \ucc28\ub294 R^2 \uc548\uc5d0\uc11c\ub9cc \uc758\ubbf8\uac00 \uc788\uc73c\ub2c8\uae4c…) \uc5b4\ub5a4 \ubc29\ubc95\uc73c\ub85c \ud480\uc5c8\ub294\uc9c0 \uad81\uae08\ud558\uad70\uc694. \uadf8\ub0e5 \uacc4\uc0b0\ud55c \uac83\uc774\ub77c\uba74 \uacc4\uc0b0\uc744 \uc8fc\uc758\ud558\uc5ec\uc57c \ud560 \uac83\uc774\uace0… \ud78c\ud2b8\uc5d0 \uc788\ub4ef\uc774 \ucc28\uc6d0\uc815\ub9ac\ub97c \uc4f0\uba74 2\ucc28\uc6d0 \uacf5\uac04\uc5d0\uc11c 2\ucc28\uc6d0 \uacf5\uac04\uc73c\ub85c\uc758 \uc0ac\uc0c1\uc774\ub2c8\uae4c onto\ub294 dim(R_T)=2 \ub77c\ub294 \ub9d0\uc774\uace0, \uc774 \ub9d0\uc740 dim(N_T)=0 \uc774\ub77c\ub294 \ub9d0\uc774\uc5b4\uc11c Tv=0 \uc744 \ud480\uc5b4\ubcf4\uc544 \ud56d\uc0c1 v=0\uc784\uc744 \ubcf4\uc774\ub77c\ub294 \ub9d0\uacfc \uac19\uc740\ub370… \uc774 \ub9d0\uc740 P1(v)=P2(v)\uc640 \uac19\uace0, P1(v)\ub294 \uc9c1\uc120 y=(1\/2)x \uc704\uc5d0 \ub193\uc774\uace0 P2(v)\ub294 y=2x \uc704\uc5d0 \ub193\uc774\ub2c8\uae4c \uc774 \ub450 \ubca1\ud130\uac00 \uac19\uc73c\ub824\uba74 P1(v)=P2(v)=0 \uc77c \ub54c \ubfd0\uc774\uc9c0\uc694. \uadf8\ub7f0 v\ub294 v=0 \ubc16\uc5d0 \uc5c6\uace0\uc694… \ub098\uc911\uc5d0 \ud480\uc774\ub97c \ubcf4\uace0 \ud2c0\ub9b0 \ubd80\ubd84\uc774 \uc5b4\ub518\uc9c0 \uc774\uc57c\uae30\ud574 \ubcf4\uc9c0\uc694. – \uae40\uc601\uc6b1 <\/p>\n

A: \uc5b4\ub5a4 \ubd80\ubd84\uc744 \uc798\ubabb \uc0dd\uac01\ud588\ub294\uc9c0 \uc54c\uc558\uc2b5\ub2c8\ub2e4. \u3160\u3160 \uc5b4\uc774\uc5c6\uac8c\ub3c4 orthogonal projection \uacfc projection \uc5d0 \ub300\ud55c \ud63c\ub3d9\uc744 \ud558\uace0 \ubb38\uc81c\ub97c \ud480\uc5c8\uc2b5\ub2c8\ub2e4.\uac1c\ub150\uc5d0 \ub300\ud55c \ud63c\ub3d9\uc774 \uc788\uc73c\ub2c8 \uc62c\ubc14\ub978 \ud480\uc774\ub97c \uc0dd\uac01\ud574\ub0b4\uc9c0 \ubabb\ud55c\uac8c \ub2f9\uc5f0\ud558\uc9c0\uc694. \uca5d…\uc55e\uc73c\ub85c\ub294 \ub354 \uc5f4\uc2ec\ud788 \uacf5\ubd80\ud574\uc57c\uaca0\uc2b5\ub2c8\ub2e4. \ub2f5\ubcc0\ud574\uc8fc\uc154\uc11c \uac10\uc0ac\ud569\ub2c8\ub2e4. ^^ (2005.06.11 \uc2e0\uc601\uc2dd) <\/p>\n

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Q(=Q1): 0\ubca1\ud130\uc5d0 \ub300\ud55c \uc9c8\ubb38\uc785\ub2c8\ub2e4. \ubca1\ud130\uacf5\uac04 X\uc758 \ubd80\ubd84\uc9d1\ud569\uc774 U\ub85c \uc815\uc758\ub418\uc5c8\uc744\ub54c, dim X = dim U + dim W – dim (U\u2229W) \uac00 \uc131\ub9bd\ud558\uace0, W\uac00 U\uc758 \uc5ec\uacf5\uac04\uc77c\ub54c\ub294 \uc6b0\ud56d\uc758 dim (U\u2229W) = 0 \uc774 \ub418\uc5b4\ubc84\ub9bd\ub2c8\ub2e4. 0\ubca1\ud130\uc758 \uacbd\uc6b0 U\uc640 W\uc5d0 \ubaa8\ub450 \uc18d\ud558\uae30\uc5d0 \uad73\uc774 \ucc28\uc6d0\uc73c\ub85c \uce5c\ub2e4\uba74 0\ucc28\uc6d0\uc774 \ub420\ud150\ub370\uc694. \ubaab\uacf5\uac04\uc758 \uacbd\uc6b0 V\/U \ub85c \ud45c\uc2dc\ub420\ub54c, \ubd80\ubd84\uacf5\uac04 U\uc758 coset \uc778 {x} \uc5d0 \uc788\uc5b4, x+U (\ub2e8, x\u22600) \uc758 \uacf5\uac04\uc740 0 \ubca1\ud130\ub97c \ud3ec\ud568\ud558\uc9c0 \uc54a\uc2b5\ub2c8\ub2e4. \uc789\uc5ec\ub958\ub4e4\uc758 \uc5f0\uc0b0\uc5d0\uc11c\ub294 0\ubca1\ud130\ub97c 0 + U = U \ub85c \uc0ac\uc6a9\ud558\ub294\ub370\uc694, \uace0\uc815\ub41c \ubca1\ud130 x\uac00 \uc788\uc73c\uba74 V\/U\uc758 {x} \uc790\uccb4\uac00 \uadf8 \ub0b4\ubd80\uc5d0\uc11c \ub367\uc148\uacfc \uc2a4\uce7c\ub77c\uacf1\uc774 \ud5c8\uc6a9\ub418\ub294 \uacf5\uac04\uc73c\ub85c \ubcfc \uc218 \uc788\ub098\uc694? (2005.6.8 \uc774\uc9c4\uc601) <\/p>\n

A(+Q)(=Q2): \uc800\ub294 \uc218\uac15\uc0dd\uc774\uc9c0\ub9cc \uac10\ud788 \ub2f5\ubcc0\uc744 \ub2ec\uc790\uba74.. (\uc8c4\uc1a1^^) \uadf8\ub7ec\ud55c \uc9d1\ud569\uc740 \ubca1\ud130\uc758 \ub367\uc148\uacfc \uc2a4\uce7c\ub77c\uacf1\uc5d0 \ub300\ud574\uc11c \ub2eb\ud600\uc788\uc9c0\uc54a\uc74c\uc744 \uc27d\uac8c \ud655\uc778\ud558\uc2e4\uc218 \uc788\uc744\uac81\ub2c8\ub2e4. \uadf8\ub798\uc11c \ubca1\ud130\uacf5\uac04\uc774 \ub420\uc218\uac00 \uc5c6\ub2e4\ub294\uad70\uc694. \ub9cc\uc57d \ubca1\ud130\uacf5\uac04\uc774 \ub418\uba74 \ubaab\uacf5\uac04\uc774\ub77c\ub294 \uc0c8\ub85c\uc6b4 \uacf5\uac04\uc744 \uc815\uc758\ud558\uc9c0 \uc54a\uc544\ub3c4 \ub420\uac83\uac19\uc740\ub370 \ub9de\ub098\uc694? \uadf8\ub7fc \uc800\ub3c4 \uad50\uc218\ub2d8\uc758 \ub2f5\ubcc0\uc744 \uae30\ub2e4\ub9ac\uaca0\uc2b5\ub2c8\ub2e4. -[wiki:WhoAmI \ub098\ub294\ub204\uad74\uae4c?] A: \uc6b0\uc120 \uc55e\uc758 \uc9c8\ubb38(Q1)\uc5d0\uc11c U\ub294 X\uc758 ”’\ubd80\ubd84\uacf5\uac04”’\uc774\ub77c\uc57c \ud558\uace0\uc694… \ud83d\ude42 \uadf8\ub7f0\ub370 Q1\uc758 \uc9c8\ubb38\uc740 \uc774\ud574\ub97c \ud558\uace0 Q2\uc758 comment\uac00 \uc633\uc9c0\ub9cc, \ubcf5\uc7a1\ud558\uac8c \ubb3c\uc5b4\ubcf8 \uac83\uc774 \ubb54\uac00 \uadf8 \uc9c8\ubb38 \ub9d0\uace0\ub3c4 \ubb3b\uace0 \uc2f6\uc740 \uac83\uc774 \uc788\ub294 \uac83 \uac19\uad70\uc694… \ubb54\uc9c0 \ubab0\ub77c\uc11c \ub2f5\uc740 \ubabb\ud558\uaca0\ub124\uc694. \ub9c8\uc9c0\ub9c9\uc73c\ub85c Q2\uc758 \ub098\uc911\uc9c8\ubb38 \ubd80\ubd84\uc740 \uc2dc\uac04\uc911\uc5d0 \ubaab\uacf5\uac04\uc744 \uc815\uc758\ud560 \ub54c \uc65c \uc774\ub7f0 \uc815\uc758\ub97c \ud558\ub294\uc9c0\uc5d0 \ub300\ud558\uc5ec \ub9ce\uc774 \uc124\uba85\ud588\uc5c8\ub294\ub370 \uadf8 \ubd80\ubd84\uc744 \uc774\ud574\ud558\uba74 \ub2f5\uc774 \ub420 \ub4ef \uc2f6\uad70\uc694. <\/p>\n

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Q: \uc30d\ub300\ubc14\ud0d5\ubca1\ud130\ub97c \uacc4\uc0b0\ud574\ubcf4\ub824\uace0 \ud588\ub294\ub370\uc694. \uc30d\ub300\ubc14\ud0d5\ubca1\ud130\uac00 \uc77c\ucc28\ud568\uc218\ub2c8\uae4c, \uc30d\ub300\ubc14\ud0d5\ubca1\ud130\uac00 \ubb34\uc5c7\uc778\uc9c0 \ubcf4\uc5ec\uc8fc\ub824\uba74 \ubca1\ud130 x\uc758 \ud568\uc218\uac12\uc774 \ubb34\uc5c7\uc778\uc9c0 \uc368\uc8fc\ub294 \ubc29\uc2dd\uc73c\ub85c \ud45c\ud604\ud574\uc57c\ud558\ub098\uc694? \uadf8\ub7ec\ub2c8\uae4c \uc30d\ub300\ubc14\ud0d5\ubca1\ud130\uac00 \uc77c\ucc28\ud568\uc218 A \ub77c\uace0 \ud558\uba74 A\uac00 \ubb34\uc5c7\uc778\uc9c0 \ubcf4\uc5ec\uc8fc\uae30 \uc704\ud574 A(x)=(\ud568\uc218\uac12) \uc774\ub7f0\uc2dd\uc73c\ub85c \ud45c\ud604\ud558\uae30\ub9cc \ud558\uba74 \ub418\ub294\uac74\uac00\uc694? <\/p>\n

A: \ubb3c\ub860 \uadf8\ub798\uc694. \ub2e4\ub978 \ubc29\ubc95\ub3c4 \uc788\uc744 \uc218 \uc788\uc9c0\ub9cc \uadf8 \ud568\uc218\ub97c \uad6c\uccb4\uc801\uc73c\ub85c(\uc2dd\uc73c\ub85c) \uc4f0\uba74 \uadf8 \uc774\uc0c1 \uc88b\uc744 \uc218\uac00 \uc5c6\uaca0\uc9c0\uc694. (\uc5ec\uae30\uc11c \ub2e4\ub978 \ubc29\ubc95\uc774\ub77c\uace0 \ud558\uba74 \uc30d\ub300\uacf5\uac04\uc758 \ubc14\ud0d5\ubca1\ud130\ub97c \ud558\ub098 \uc54c\uace0 \uc788\uc744 \ub54c\ub294 \uadf8 \ubc14\ud0d5\ubca1\ud130\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \ub3c4 \uc788\uc744 \uac83\uc774\uace0… \ub4f1\ub4f1 \uc0c1\ud669\uc5d0 \ub530\ub77c \ub2e4\ub978 \ubc29\ubc95\ub3c4 \uc788\uc744 \uc218 \uc788\ub2e4\ub294 \uac81\ub2c8\ub2e4.) – \uae40\uc601\uc6b1 <\/p>\n

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Q: \ub2e4\ud56d\uc2dd\uc758 \uc9d1\ud569\uc778 $ \\mathcal{P}_n $ \uc5d0 \ub300\ud574 \uc9c8\ubb38 \uc788\ub294\ub370\uc694. \uac00\ub839 $ \\mathcal{P}_2 $ \uc774\uba74, $ a_0 + a_1 x + a_2 x^2 $ \ub85c \ud45c\ud604\ub418\uace0, \uc774\ub294 $ \\mathbb{R}^3 $ \uacfc \ub3d9\ud615\uc0ac\uc0c1\uc744 \ucc3e\uc744 \uc218 \uc788\ub2e4\uace0 \ud558\uc168\ub294\ub370\uc694. \ub2e4\ud56d\uc2dd\uc758 \uc9d1\ud569\uc778 $ \\mathcal{P}_2 $ \uc5d0\uc11c $ x^2 $ \uc758 \uacc4\uc218\uac00 0\uc778 1\ucc28 \uc774\ud558\uc758 \ub2e4\ud56d\uc2dd\ub4e4\ub3c4 \uc774 \uc9d1\ud569\uc5d0 \ud3ec\ud568\uc774 \ub418\ub294\uac74\uac00\uc694? \uc911\uace0\ub4f1\ud559\uad50\uc5d0\uc11c\ubd80\ud130 2\ucc28 \ubc29\uc815\uc2dd\uc758 \uacbd\uc6b0 $ x^2 $ \uc55e\uc5d0\ub294 0\uc774 \uc62c \uc218 \uc5c6\ub2e4\ub294 \uad00\ub150\uc774 \uc788\uc5b4\uc11c\uc694. (2005.06.03 \uc774\uc9c4\uc601) <\/p>\n

A: \ubb3c\ub860\uc774\uc608\uc694. \uadf8\ub798\uc11c \uc6b0\ub9ac\uac00 $ \\mathcal{P}_2 $ \ub97c \uc815\uc758\ud560 \ub54c \uc774 \uacf5\uac04\uc740 2\ucc28 \uc774\ud558\uc758 \ucc28\uc218\ub97c \uac00\uc9c0\ub294 \ub2e4\ud56d\uc2dd\uc774\ub77c\uace0 \ud588\uace0\uc694, \uadf8\ub0e5 \uc774\ucc28\ub2e4\ud56d\uc2dd\uc758 \uc9d1\ud569\uc774\ub77c\uace0 \ud558\uc9c0 \uc54a\uc558\uc5c8\uc5b4\uc694. \ub530\ub77c\uc11c \uc774\ucc28\ud56d\uc758 \uacc4\uc218\uac00 0\uc774 \ub418\uc5b4 \uc2e4\uc81c\ub85c\ub294 1\ucc28\ub2e4\ud56d\uc2dd\uc774\ub098 0\ucc28\ub2e4\ud56d\uc2dd(\uc0c1\uc218\ub2e4\ud56d\uc2dd)\uc778 \uacbd\uc6b0\uc5d0\ub3c4 \ubaa8\ub450 $ \\mathcal{P}_2 $ \uc758 \uc6d0\uc18c\uac00 \ub41c\ub2f5\ub2c8\ub2e4. – \uae40\uc601\uc6b1 <\/p>\n

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Q : \ud654\uc0b4\ud45c\ub97c \ubca1\ud130\ub85c \uc0dd\uac01\ud560 \ub54c basis \ud654\uc0b4\ud45c\ub4e4\ub85c \uae30\ud558\ud559\uc801\uc73c\ub85c \ud45c\ud604\ud558\ub294 \uac83\ucc98\ub7fc Dual space \uc548\uc758 \ubca1\ud130\ub4e4\ub3c4 Dual basis \ub85c \uae30\ud558\ud559\uc801\uc73c\ub85c \ud45c\ud604\ud560 \uc218 \uc788\ub098\uc694? <\/p>\n

A: 1\ucc28\ud568\uc218 $ ax+by $ \ub97c \uac04\ub2e8\ud788 1\ucc28\ud568\uc218 $ (a,b) $ \ub77c\uace0 \uc4f0\uae30\ub85c \ud558\uba74, $ (a,b) $ \ub3c4 \uae30\ud558\ud559\uc801\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218\ub294 \uc788\uc9c0\uc694. \uc774\ub7f0 \ub2f5\uc744 \uc6d0\ud558\ub294 \uac74\uc9c0? \uc544\ub2c8\uba74 \ubb54\uac00 \ub354 \uae30\ud558\ud559\uc801\uc73c\ub85c \ub098\ud0c0\ub0b4\uae30 \ud798\ub4e0 \uac83\uc744 \uc0dd\uac01\ud558\uace0 \uc788\ub294\uac74\uc9c0? \uacc4\uc18d \ubc11\uc5d0 \ub2ec\uc544\uc11c \uc9c8\ubb38\ud574\uc694… – \uae40\uc601\uc6b1 <\/p>\n

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Q: (\ub178\ud2b8 p19. \uc14b\uc9f8\uc904) \u03b11,\u03b12,.. \ub97c x\uc758 \ud568\uc218\ub77c\uace0 \ud55c \ubd80\ubd84\uc5d0\uc11c ”’x1,x2,..\ub97c \uace0\uc815\uc2dc\ucf1c \ub193\uace0”’ x\ub97c \ubcc0\ud654\uc2dc\ud0a4\uba74 \u03b11,\u03b12,..\uac00 \ubcc0\ud558\uae30 \ub54c\ubb38\uc5d0 \u03b11,\u03b12,..\ub97c x\uc758 \ud568\uc218\ub77c\uace0 \ud55c \uac74\uac00\uc694? <\/p>\n

A: That’s right. \ubc14\ub85c \uadf8\uac70\uc608\uc694. – \uae40\uc601\uc6b1 Q: \uadf8\ub807\ub2e4\uba74 x\uac00 n\uac1c\uc758 component\ub85c \uc774\ub8e8\uc5b4\uc84c\uc73c\ub2c8\uae4c \u03b1\ub294 \ubcc0\uc218\uac00 n\uac1c\uc778 \ud568\uc218\uac00 \ub418\ub294\uac70\uc8e0? <\/p>\n

A: $ x $ \uac00 $ n $ \ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc758 \ubca1\ud130\ub77c\uace0 \uaf2d $ \\mathbb{R}^n $ \uc758 \ubca1\ud130\ub294 \uc544\ub2c8\uac70\ub4e0\uc694. \uadf8\ub798\uc11c $ x=(x_1,…,x_n) $ \uc778 \uacbd\uc6b0\uc5d0\ub294 \ubcc0\uc218\uac00 \uc2e4\ubcc0\uc218 $ n $ \uac1c\ub77c\uace0 \ud574\ub3c4 \uc88b\uc9c0\ub9cc \uadf8\ub807\uc9c0 \uc54a\uace0 \ubca1\ud130\uac00 \ub2e4\ud56d\uc2dd\uc774\ub77c\ub358\uac00 \uadf8\ub7f0 \uc77c\ubc18\uc801\uc778 \uacbd\uc6b0\uc5d0\ub294 \ubcc0\uc218\ub294 \uadf8\ub0e5 \ud55c\uac1c\ub77c\uace0 \ud558\ub294 \uac83\uc774 \ub354 \ub9de\uc744 \uac83 \uac19\uc560\uc694. \uc2e4\uc81c\ub85c \ubcc0\uc218\uc758 \uac1c\uc218\ub294 \uadf8\ub9ac \uc911\uc694\ud558\uc9c0 \uc54a\uace0\uc694, \uc911\uc694\ud55c \uac83\uc740 \ubcc0\uc218 \uc804\uccb4\uac00 \uc774\ub8e8\ub294 \uacf5\uac04\uc758 \ucc28\uc6d0\uc774\uc9c0\uc694. <\/p>\n

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Q : \uc880 \uc5c9\ub6b1\ud55c \uc9c8\ubb38\uc778\ub370\uc694. \ub450 \ud589\ub82c\uc744 \uacf1\ud560 \ub54c ‘\ud589’\uc758 \uc131\ubd84\uacfc ‘\uc5f4’\uc758 \uc131\ubd84\uc744 \uacf1\ud558\uc5ec \ub354\ud558\ub294 \uc791\uc5c5\uc744 \ud558\uac8c \ub418\ub294\ub370, \ub9cc\uc57d \uc774\uac83\uc744 \uc870\uae08 \ubc14\uafb8\uc5b4\uc11c \uacf1\uc148\uc774 ‘\ud589’\uc758 \uc131\ubd84\uacfc ‘\ud589’\uc758 \uc131\ubd84\uc744 \uacf1\ud558\uc5ec \ub354\ud558\ub294 \uac83\uc73c\ub85c \uc815\uc758\ud558\uba74 \uc5b4\ub5a4 \uc548\uc88b\uc740 \uc131\uc9c8\uc744 \uac16\uac8c \ub418\ub098\uc694? \uc989 \ud589\ub82c\uc758 \uacf1\uc148\uc5d0\uc11c \uc131\ubd84\ub07c\ub9ac \uacf1\ud558\uc5ec \ub354\ud558\ub294 \uac83 \uc790\uccb4\uc5d0\ub294 \uad00\uc2ec\uc774 \uc5c6\uace0\uc694. \uc65c ‘\ud589’\uacfc’\uc5f4’\uc744 \uc9dd\uc9c0\uc5b4\uc11c \uacc4\uc0b0\ud558\uace0 ‘\ud589’\uacfc ‘\ud589’\uc744 \uc9dd\uc9d3\uc9c0 \uc54a\ub294 \uac83\uc778\uc9c0\ub97c \uc54c\uace0\uc2f6\uc2b5\ub2c8\ub2e4. – WhoAmI <\/p>\n

A: \uc0dd\uac01\ud574 \ubcf4\ub2c8 \uc88b\uc740 \uc9c8\ubb38\uc774\uad70\uc694. \ud83d\ude42 \ub450 \ud589\ub82c $ A,B$ \uc5d0\uc11c $ A$ \uc758 i\ud589\uacfc $ B$ \uc758 j\ud589\uc744 \ub0b4\uc801\ud55c \uac12\uc744 ij-\uc131\ubd84\uc73c\ub85c \ud558\ub294 \ud589\ub82c\uc744 \ub9cc\ub4e4\uba74 \uc774 \ud589\ub82c\uc740 \uc2e4\uc81c\ub85c\ub294 $ AB^T$ \ub791 \ub611\uac19\uc544\uc694. \ud589\ub82c\uc758 \uacf1\uc148\uc744 \uc774\ub807\uac8c \uc4f0\uae30\ub85c \ud574\ub3c4 \uc548\ub420 \uac83\uc740 \uc5c6\ub294\ub370 \uc9c0\uae08 \ud558\ub294 \uac83\uc774\ub791 \ub0b4\uc6a9\uc774 \ub2e4\ub978 \uac83\uc740 \ud558\ub098\ub3c4 \uc5c6\uace0\uc694…(\uc989 \uc9c0\uae08 \uc774\ub860\ud558\uace0 isomorphic\ud55c \uc774\ub860\uc774 \uc0dd\uae30\uace0\uc694) \uadf8\ub7f0\ub370 \uc6b0\ub9ac \ubc29\uc2dd\uc774 \uc2e4\uc81c\ub85c \uacf1\uc148\uc744 \ubcf4\ub294\ub370 \uc870\uae08 \ub354 \ud3b8\ub9ac\ud558\uc9c0\uc694. – \uae40\uc601\uc6b1 <\/p>\n

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Q:\ub178\ud2b87\ucabd\uc758 \ub3c4\uc6c0\uc815\ub9ac 1.2\uc5d0 \ub300\ud55c \uc99d\uba85\uc5d0\uc11c 8\ubc88\uc9f8\uc904\uc5d0 “k>n\uc774\uc5c8\ub2e4\uace0 \uac00\uc815\ud558\uba74 y1,y2…yk\ub294 \uc77c\ucc28\uc885\uc18d\uc774 \ub420\uc218 \ubc16\uc5d0 \uc5c6\uc73c\uba70” \ub77c\uace0 \ub418\uc5b4\uc788\ub294\ub370\uc694. \uc99d\uba85\ud558\ub824\ub294 \uba85\uc81c\ub294 “y1,y2…yk\uac00 \uc77c\ucc28\ub3c5\ub9bd\uc77c\ub54c k<=n \uc774\ub2e4.”\uc778\ub370 \uc774\uac83\uacfc 8\ubc88\uc9f8\uc904\uc5d0 \uc368\uc788\ub294 \uba85\uc81c\uc640 \ub300\uc6b0\uad00\uacc4\uc5ec\uc11c \ub3d9\uce58\uc778\uac83\uac19\uc2b5\ub2c8\ub2e4. \uba85\uc81c\ub97c \uc99d\uba85\ud560 \ub54c \uadf8 \uba85\uc81c\uc640 \ub3d9\uce58\uc778 \uba85\uc81c\ub97c \uc774\uc6a9\ud560\uc218\ub294 \uc5c6\ub294\ub370, \ub178\ud2b8\uc758 \uc99d\uba85\uc774 \uc798\ubabb\ub418\uc5c8\uc744\ub9ac\ub294 \uc5c6\uace0, \uc81c\uac00 \uc5b4\ub290\ubd80\ubd84\uc744 \ud30c\uc545\ud558\uc9c0 \ubabb\ud55c\uac74\uac00\uc694? <\/p>\n

A: \uba85\uc81c \uc790\uccb4\ub97c \ub300\uc6b0\uba85\uc81c\ub85c \ubc14\uafd4\uc11c \uc99d\uba85\ud558\uae30\ub294 \ud798\ub4e4\uad6c\uc694, \uc815\ub9ac\uc911, Linearly dependent iff at least one of vectors is expressible as a linear combination of the other vectors in ~<\/code> \ub97c \uc774\uc6a9\ud558\uba74, k>n \uc77c\ub54c \uc885\uc18d\uad00\uacc4\uac00 \ud655\uc2e4\ud558\uac8c \uc99d\uba85\ub418\ub124\uc694. \uc774\uac83\uc758 \uc99d\uba85\uc740 \uc218\uc5c5\uc2dc\uac04\uc5d0 \ub2e4\ub918\uad6c\uc694. Q2: \uadf8\ub807\ub2e4\uba74 “k>n\uc774\uc5c8\ub2e4\uace0 \uac00\uc815\ud558\uba74 y1,y2…yk\ub294 \uc77c\ucc28\uc885\uc18d\uc774 \ub420\uc218 \ubc16\uc5d0 \uc5c6\uc73c\uba70” \uc774\uac83\uacfc “y1,y2…yk\uac00 \uc77c\ucc28\ub3c5\ub9bd\uc77c\ub54c k<=n \uc774\ub2e4.” \uc774\uac83\uc740 \ub3d9\uce58\uad00\uacc4\uac00 \uc544\ub2cc\uac00\uc694? \ub178\ud2b8\uc758 \uc99d\uba85\uc740 \uc798\ubabb\uc774 \uc5c6\ub294\uac74\uac00\uc694? A: \ub3d9\uce58 \uad00\uacc4\ub97c \uc774\uc6a9\ud574\uc11c \uc99d\uba85\uc744 \ud558\ub294 \uacbd\uc6b0\ub3c4 \uc788\uc8e0? \ub2e4\uc2dc \uc6d0\uc810\uc73c\ub85c \ub3cc\uc544\uc640\uc11c\uc694, \ub178\ud2b87\ucabd\uc758 \uc99d\uba85 \ubc29\ubc95\uc740, \ub300\uc6b0\uba85\uc81c\ub97c \uc99d\uba85\ud558\ub294\uac8c \uc544\ub2cc\ub370\uc694, \uac00\uc815\uc744 k\u2265n(k=n \uc774\ub780 \ud45c\ud604\uc774 \ub0ab\uc9c0 \uc54a\uc740\uc9c0?),\uc77c\ub54c n-1 \ubc88\uc758 y\ub97c \ud45c\ud604\ud558\uba74, $ \\{y_1,y_2,…,y_n\\}$ \ub97c \uc0dd\uc131\ud560 \uc218 \uc788\uace0, \uc774\ub54c\uac00 k=n \uc774 \ub418\uaca0\uad70\uc694, \ud558\uc9c0\ub9cc, k > n \uc77c\ub550, \ubaa8\uc21c\uc774 \ub418\uaca0\uc8e0? (\uc0dd\uc131\ub41c \ubca1\ud130\ub294 \ubc18\ub4dc\uc2dc V\ub97c span \ud574\uc57c \ud569\ub2c8\ub2e4. \ubd80\ubd84 \uacf5\uac04\uc774\uba74 \uc548 \ub418\uc8e0.) \uadf8\ub798\uc11c, k \u2264 n \uc73c\ub85c \uc99d\uba85\uc774 \ub05d\ub0a9\ub2c8\ub2e4. Q: \ube60\ub974\uac8c \ub2f5\ubcc0\ud574\uc8fc\uc154\uc11c \uac10\uc0ac\ud569\ub2c8\ub2e4. \uadf8\ub7f0\ub370k > n \uc77c\ub54c \uc77c\ucc28\ub3c5\ub9bd\uc744 \uc774\ub8e8\ub294 \ubca1\ud130\uac00 \uc77c\ucc28\uc885\uc18d\uc744 \uc774\ub8e8\ub294 \ubca1\ud130\uc218\ubcf4\ub2e4 \ucee4\uc9c4\ub2e4\ub294 \uac83\uc774 \ubb34\uc2a8 \ub73b\uc778\uc9c0 \uc798 \ud30c\uc545\ud558\uc9c0\ubabb\ud558\uaca0\uc5b4\uc694. A: \uc77c\ucc28\ub3c5\ub9bd\uc744 \uc774\ub8e8\ub294 \ubca1\ud130\uac00 $ \\{y_1,y_2,…,y_k\\}$ \ub85c \ub098\ud0c0\ub0b4\uc5b4\uc9c0\uace0, \uc774\ubcf4\ub2e4 \ubca1\ud130\uc758 \uac1c\uc218\uac00 \uc791\uc740 $ \\{y_1,y_2,…,y_n\\}$ \uc774\uba74 V\ub97c span\ud558\uc9c0 \ubabb\ud558\uc8e0, \uadf8\ub7fc \uc804\uc81c\uc5d0 \ubaa8\uc21c\uc774 \ub418\uaca0\uc8e0.(\uc717\ubd80\ubd84 \ud45c\ud604\uc774 \ubd80\uc801\uc808\ud574\uc11c \uc0ad\uc81c\ud588\uc2b5\ub2c8\ub2e4.) <\/p>\n

A: \uc6b0\uc120 \uccab\uc9f8 \ub2f5\ubcc0\uc740 \uc633\uc2b5\ub2c8\ub2e4. \uadf8\ub9ac\uace0 \ub458\uc9f8 \uc9c8\ubb38(Q2)\uc740 \uba85\uc81c\uac00 “\uc774 \ub54c, $ k>n$ \uc774\uc5c8\ub2e4\uace0 \uac00\uc815\ud558\uba74 $ y_1,y_2,…,y_k$ \ub294 \uc77c\ucc28\uc885\uc18d\uc774 \ub420\uc218 \ubc16\uc5d0 \uc5c6\uc73c\uba70”\ub85c \ub418\uc5b4 \uc788\uc73c\uba70 “(\ud56d\uc0c1) $ k>n$ \uc774\uc5c8\ub2e4\uace0 \uac00\uc815\ud558\uba74 $ y_1,y_2,…,y_k$ \ub294 \uc77c\ucc28\uc885\uc18d\uc774 \ub420\uc218 \ubc16\uc5d0 \uc5c6\uc73c\uba70”\uc774\ub780 \ub73b\uc774 \uc544\ub2d9\ub2c8\ub2e4. \uc989 \uc99d\uba85 \uacfc\uc815\uc5d0\uc11c $ \\{y_1,y_2,…,y_n\\}$ \uc774 $ V$ \ub97c span\ud568\uc744 \uc54c\uac8c \ub418\uc5c8\uc744 \ub54c $ k>n$ \uc774 \ub41c\ub2e4\uace0 \uac00\uc815\ud558\uba74 \ubaa8\uc21c\uc774\ub77c\ub294 \ub9d0\uc785\ub2c8\ub2e4. \ub3c4\uc6c0\uc815\ub9ac\uc758 \uba85\uc81c\uc758 \ub300\uc6b0\uc778 \ud56d\uc0c1… \uadf8\ub7ec\ud558\ub2e4\ub294 \ub9d0\uacfc\ub294 \ub2e4\ub978 \ub73b\uc774\uc9c0\uc694. ”’\uadf8\ub098\uc800\ub098 \uc9c8\ubb38\ud55c \uce5c\uad6c\ub294 \ub204\uad6c\uace0, \ub2f5\ubcc0\ud55c \uce5c\uad6c\ub294 \ub204\uad70\uac00\uc694?”’ – \uae40\uc601\uc6b1 <\/p>\n

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Q : \uad50\uacfc\uc11c 9\ud310 238\ucabd\uc758 1.(e) \uc5d0 \ub300\ud55c \ubb38\uc758\uc785\ub2c8\ub2e4. $ \\mathbb{R}^3$ \uc758 \ubd80\ubd84\uacf5\uac04\uc5d0 \ub300\ud55c \uc9c8\ubb38\uc778\ub370\uc694. all vectors of the form (a, b, 0) \uc5d0\uc11c 5.2.1 Theorem \uc758 addition, multiplication of scalar k \uac00 \ubaa8\ub450 \ub9cc\uc871\ud558\ub294\ub370, \uc815\ub2f5\uc740 (e) \uac00 \ud3ec\ud568\uc774 \ub418\uc5b4\uc788\uc9c8 \uc54a\ub124\uc694. \uc81c\uac00 \uc774\uc0c1\ud55c\uac74\uc9c0? <\/p>\n

\uadf8\ub9ac\uace0, 5\ubc88\uc758 (a) \uc5d0\uc11c tr(A)\uac00 \uc758\ubbf8\ud558\ub294 \uac83\uc740 \ubb34\uc5c7\uc774\uc8e0? (upper triangular form or lower triangular form?) \uc81c\uac00 \uc218\uc5c5\uc2dc\uac04\uc5d0 \ubabb\ub4e4\uc5b4\uc11c \ubaa8\ub974\ub294\uac74\uac00\uc694..? (05\/04\/20 -\uc774\uc9c4\uc601) <\/p>\n

A: \uc6b0\uc120 \uc55e\uc758 1.(e)\ub294 \uc9c0\uae08 \uad50\uacfc\uc11c\uac00 \uc5c6\uc5b4\uc11c \uc54c \uc218\uac00 \uc5c6\ub124\uc694. \ub4a4\uc758 5\ubc88\uc758 tr(A)\ub294 A\uc758 trace\uc785\ub2c8\ub2e4. \uc218\uc5c5\uc2dc\uac04\uc5d0 \uc548 \ud588\uc5b4\uc694… – \uae40\uc601\uc6b1 <\/p>\n

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Q : \uc624\ub298 \uc218\uc5c5\uc2dc\uac04 \ub54c \uc2dc\ud5d8\ubb38\uc81c\uac00 \uad50\uacfc\uc11c\uc758 \uc5f0\uc2b5\ubb38\uc81c\uc640\ub294 \ub2e4\ub978 \ud615\ud0dc\uc758 \ubb38\uc81c\ub77c\uace0 \ud558\uc168\ub294\ub370\uc694. \uadf8\ub7ec\uba74 \ub178\ud2b8\uc5d0 \uc788\ub294 \ubb38\uc81c\ub294 \uc2dc\ud5d8\ubb38\uc81c\uc640 \ube44\uad50\ud588\uc744\ub54c \uc0c1\ub300\uc801\uc73c\ub85c(\uad50\uacfc\uc11c\uc758 \uc5f0\uc2b5\ubb38\uc81c\uc5d0 \ube44\ud574) \ub354 \ube44\uc2b7\ud55c\uac00\uc694? \uadf8\ub9ac\uace0 \uc2dc\ud5d8\ubb38\uc81c\uc640 \uad50\uacfc\uc11c\uc5f0\uc2b5\ubb38\uc81c\uc758 \ucc28\uc774\uc810\uc774, \uc2dc\ud5d8\ubb38\uc81c\ub294 \ucc45\uc758 \ub3c4\uc6c0 \uc5c6\uc774 \uc815\uc758\ub098 \uc815\ub9ac\ub97c \uc0dd\uac01\ud574\ub0b4\uc5b4 \uc815\ud655\ud788 \uc774\uc6a9\ud560\uc218 \uc788\uc5b4\uc57c\ud480\uc218\uc788\uace0, \uad50\uacfc\uc11c \uc5f0\uc2b5\ubb38\uc81c\ub294 \ub2e8\uc21c\ud788 \uc815\uc758\ub098 \uc815\ub9ac\ub97c \uc801\uc6a9\ud558\uba74 \ud480 \uc218\uc788\ub2e4\ub294 \uac83\uc758 \ucc28\uc774\uc810\uc778\uc9c0\ub3c4 \uc54c\uace0\uc2f6\uc2b5\ub2c8\ub2e4.(050419-\uc774\ud638\uc9c4) <\/p>\n

A: \ub2e4\ub978 \ud615\ud0dc\ub77c\uace0 \ud560 \uc218\ub294 \uc5c6\uc9c0\ub9cc \ub611\uac19\uc740 \uc720\ud615\uc758 \ubb38\uc81c\ub97c \uc22b\uc790\ub9cc \ubc14\uafbc\ub2e4\uac70\ub098 \ud558\uc9c0\ub294 \uc54a\ub294\ub2e4\ub294 \ub9d0\uc785\ub2c8\ub2e4. \uc5b4\ub5a4 \ubb38\uc81c\ub294 \uad50\uacfc\uc11c \ubb38\uc81c\uc640 \uc720\uc0ac\ud558\uac8c \ubcf4\uc77c \uc218\ub3c4 \uc788\uace0 \uc5b4\ub5a4 \uac83\uc740 \ub178\ud2b8\uc758 \ubb38\uc81c\uc5d0 \ub354 \uac00\uae4c\uc6cc \ubcf4\uc77c \uc218\ub3c4 \uc788\uc9c0\uc694. \ubb3c\ub860 \ube44\uc2b7\ud55c \ubb38\uc81c\uac00 \ud558\ub098\ub3c4 \uc5c6\ub294 \uac83\ub3c4 \uc544\ub2c8\uace0\uc694… \ud83d\ude42 \uc624\ud788\ub824 \ub354 \ud63c\ub780\uc2a4\ub7fd\uac8c \ubcf4\uc77c \uac83 \uac19\ub124\uc694. \uc5b4\ub5bb\uac8c \ubcf4\uba74 \uad50\uacfc\uc11c\uc758 \uc5f0\uc2b5\ubb38\uc81c\uc640 \ub300\ub3d9\uc18c\uc774\ud558\uc9c0\ub9cc \uc0c8\ub85c\uc6b4 \ubb38\uc81c\ub3c4 \uc788\ub2e4\ub294 \uc815\ub3c4\uc785\ub2c8\ub2e4. \uacf5\ubd80\ud55c \uac83\uacfc \uaf2d \uac19\uc740 \ud615\ud0dc\uc758 \ubb38\uc81c\ub9cc \ub098\uc628\ub2e4\uace0 \uc0dd\uac01\ud560\uae4c\ubd10 \ud55c \ub9d0\uc774\uc5c8\uc5b4\uc694. – \uae40\uc601\uc6b1 <\/p>\n

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Q: 1. space\uc640 field\uc758 \ucc28\uc774 <\/p>\n

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  1. vector space\ub294 vertor\ub4e4\uc758 \ud569\uacfc \uc2a4\uce7c\ub77c\ubc30\uac00 \uc815\uc758\uc5b4 \uc788\ub294 \uacf5\uac04\uc774\ub2e4. \uc774\uac83\uc740 \ubca1\ud130\uac00 n-tuple\uc758 linear combination\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uadf8\ub807\uae30 \ub54c\ubb38\uc5d0 \uc774\uac83\ub4e4\uc740 spanning \ud560 \uc218 \uc788\ub2e4.<\/li>\n<\/ol>\n

    vector space\uc5d0\uc11c\uc758 dimention\uc740 n-tuple\uc5d0\uc11c n \uc774\uba70 \uc774\uac83\uc740 \uace0\uc815\ub418\uc5b4\uc788\ub2e4. (\ub367\uc148\uc5d0 \ub300\ud558\uc5ec \ub2eb\ud78c \uacf5\uac04\uc774\ubbc0\ub85c.) <\/p>\n

    \uadf8\ub9ac\uace0 vector field\ub294 vector\ub4e4\uc758 \ud569\uacfc scalar multiplation, \uc774\ub4e4\uc758 innerproduct\uc640 outer product, \uc989 \ubca1\ud130\uc758 \uc678\uc801\uacfc \ub0b4\uc801\uc774 \uc815\uc758\ub41c \uacf5\uac04\uc774\ub2e4. vector \uac04\uc758 \uacf1\uc774 \uc815\uc758\ub418\uc5b4\uc57c \ud558\uae30 \ub54c\ubb38\uc5d0 \uc774\uc5d0 \uc55e\uc11c\uc11c gradient\uc640 \uc5f0\uc18d\uc131, \uadf8\ub9ac\uace0 \ubbf8\ubd84\uac00\ub2a5\uc131 \ub4f1\uc774 \uc815\uc758\ub418\uc5b4\uc57c \ud55c\ub2e4. <\/p>\n

    2\ubc88\uc740 \uacf5\ubd80\ud558\ub2e4\uac00 \uac11\uc790\uae30 \uc758\ubb38\uc774 \uc0dd\uaca8 \uba87\uc2dc\uac04\ub3d9\uc548 \uace0\ubbfc\ud558\ub2e4\uac00 \uc544\uc9c1 \uacb0\ub860\uc740 \uc774\uc815\ub3c4 \ub0ac\ub294\ub370\uc694… \uc81c \uc0dd\uac01\uc774 \uc5bc\ub9c8\ub098 \uc5b4\ub514\uc5d0\uc11c \uc798\ubabb\ub41c \uac83\uc778\uc9c0 \uc54c\uace0 \uc2f6\uad6c\uc694.. 1\ubc88\uc740 \uc5b4\ub5bb\uac8c \uc77c\ubc18\uc801\uc73c\ub85c \uc815\uc758 \ub0b4\ub9ac\uace0 \ube44\uad50\ud560 \uc218 \uc788\ub294 \uac83\uc778\uc9c0 \uc54c\uace0 \uc2f6\uc2b5\ub2c8\ub2e4. <\/p>\n

    A: \uc6b0\uc120 field\ub294 \ub367\uc148\uacfc \uacf1\uc148\uc774 \uc815\uc758\ub418\uc5b4 \uc788\uc5b4\uc57c \ud558\ub294 \uac83\uc774\ubbc0\ub85c space\uc640\ub294 \ub2e4\ub985\ub2c8\ub2e4.(space\uc5d0\ub294 \uc2a4\uce7c\ub77c\ubc30\ub9cc \uc788\uc9c0, \ub450 \ubca1\ud130\uc758 \uacf1\uc740 \uc815\uc758\ub418\uc5b4 \uc788\uc9c0 \uc54a\uc2b5\ub2c8\ub2e4.) \uadf8\ub7ec\ub098 \ubaa8\ub4e0 field\ub294 \uc790\uae30 \uc790\uc2e0\uc744 \uc2a4\uce7c\ub77c\ub85c \ud574\uc11c vector space\uac00 \ub429\ub2c8\ub2e4.(1\ucc28\uc6d0\uc774\uc8e0.) 2\ubc88\uc5d0\uc11c n-tuple\uc774\ub77c \ud558\uba74 \uc2a4\uce7c\ub77c\uc758 n-tuple\uc744 \uc774\uc57c\uae30\ud558\ub294 \uac83\uc778\uc9c0? \ubca1\ud130\uac00\uc6b4\ub370\ub294 n-tuple\uc774 \uc544\ub2cc \ubca1\ud130\ub4e4\ub3c4 \ub9ce\uc774 \uc788\uc73c\ub2c8\uae4c… \uc774 \uc774\uc57c\uae30\ub294 $ \\mathbb{R}^n$ \uc758 \uacbd\uc6b0\ub77c\uba74 \ub9de\ub294 \ub9d0\uc785\ub2c8\ub2e4. \uadf8\ub9ac\uace0 \uc14b\uc9f8\ub85c \uc6b0\ub9ac\ub294 vector field\ub294 \uc774\uc57c\uae30\ud55c \uc801\uc774 \uc5c6\ub294\ub370… \ubb34\uc2a8 \ub2e4\ub978 \uac83\uc744 \uc774\uc57c\uae30\ud558\ub294 \uac83 \uac19\uae30\ub3c4 \ud558\uace0…(\uc560\ub9e4~) – \uae40\uc601\uc6b1 <\/p>\n

    \n

    Q: \uc774\ubc88\uc8fc \ubaa9\uc694\uc77c \uc218\uc5c5\ub0b4\uc6a9\uc911\uc5d0 \uc815\ub9ac\ub97c \uc99d\uba85\ud558\ub294 \uac83\uc774 \uc788\uc5c8\ub294\ub370 \uc5b4\ub5a4 \uc815\ub9ac\uc600\ub294\uc9c0 \uc54c\uace0\uc2f6\uc2b5\ub2c8\ub2e4.\ud544\uae30\ub97c \ud558\uc9c0 \ubabb\ud574\uc11c \uae30\uc5b5\uc774 \ub098\uc9c8 \uc54a\ub124\uc694. {x1,x2,x3,…,xn} {y1,y2,y3,…,yn} \uc774\ub7f0\uac8c \ub098\uc624\uba74\uc11c x1\uacfc y1 \uc790\ub9ac\ub97c \ubc14\uafb8\uae30\ub3c4\ud558\uba74\uc11c \uc99d\uba85\uc774 \ub418\uc5c8\ub358 \uac83 \uac19\uc740\ub370 \uad50\uacfc\uc11c\ub098 \ubd80\uad50\uc7ac\uc5d0\uc11c \ucc3e\uae30\uac00 \uc5b4\ub824\uc6cc \ubd80\ud0c1\ub4dc\ub9bd\ub2c8\ub2e4. \uadf8\ub9ac\uace0 \uc2dc\ud5d8\uc5d0\uc11c \ub098\uc624\uac8c \uc99d\uba85\ubb38\uc81c\uc5d0 \uad00\ud574\uc11c \uad81\uae08\ud55c \uac83\uc774 \uc788\ub294\ub370\uc694. \uc99d\uba85\uc744 \uc804\uac1c\ud574\ub098\uac08\ub54c \uc5b4\ub5a4 \uc815\ub9ac\uac00 \ud544\uc694\ud55c \uacbd\uc6b0, \uadf8 \uc5b4\ub5a4 \uc815\ub9ac\ub97c \uc99d\uba85\ud558\uc9c0\uc54a\uace0 ‘\uc774 \uc815\ub9ac\uc5d0 \uc758\ud574\uc11c \uc774\ub807\ub2e4’\uace0 \ubc14\ub85c \uc368\ub3c4 \ub418\ub294\uac83\uc778\uc9c0 \uad81\uae08\ud569\ub2c8\ub2e4. (20050416-\uc774\ud638\uc9c4) <\/p>\n

    A: \uc774 \uc815\ub9ac\ub294 $ \\{x_1,x_2,…,x_n\\}, \\{y_1,y_2,…,y_k\\}$ \uc5d0 \ub300\ud55c \uac83\uc774\uace0\uc694… \uc99d\uba85\uc740 \ubd80\uad50\uc7ac \ub178\ud2b8\uc758 \ub3c4\uc6c0\uc815\ub9ac 1.2 (7\ucabd)\uc5d0 \uc788\uc2b5\ub2c8\ub2e4. \uc99d\uba85\uc740 \uc9e7\uc544\ubcf4\uc774\uc9c0\ub9cc argument \ubcf4\ucda9\uc774 \ubc11\uc758 footnote\uc5d0 \uc788\uc2b5\ub2c8\ub2e4. \uc99d\uba85\uc744 \ud574 \ub098\uac08 \ub54c \ud544\uc694\ud55c \uc815\ub9ac\ub294 \uc0ac\uc6a9\ud558\uc5ec\ub3c4 \ub429\ub2c8\ub2e4. \uc815\ub9ac\ub97c \uc0ac\uc6a9\ud558\uae30\ub97c \uc6d0\uce58 \uc54a\uc73c\uba74 ”’\uc815\uc758\ub85c\ubd80\ud130 \uc99d\uba85\ud558\uc5ec\ub77c”’\ub77c\ub294 \ub9e1\uc774 \ubb38\uc81c\uc5d0 \ub4e4\uc5b4 \uc788\uc744\uac81\ub2c8\ub2e4. <\/p>\n

    \n

    Q: transpose matrix\ub294 \uc5b4\ub5a4\uacf3\uc5d0 \uc0ac\uc6a9\ub418\ub294\uc9c0\uc640 \uc120\ud615\ub300\uc218\uc5d0\uc11c \uc5b4\ub5a4\uc758\ubbf8\ub97c \uac00\uc9c0\uace0 \uc788\ub294\uc9c0\ub97c \uc54c\uace0\uc2f6\uc2b5\ub2c8\ub2e4.(20050318-\uc815\ud638) <\/p>\n

    A: \uac15\uc758\ub97c \uc218\uac15\ud558\ub294 \ud559\uc0dd\uc778\uac00\uc694. \uadf8\ub7ec\uba74 \uc870\uae08 \uae30\ub2e4\ub824\uc57c \ud560 \uac70\uace0\uc694. \uc548\uadf8\ub7ec\uba74… \u3160.\u3160 \uac04\ub2e8\ud788 \uc5ec\uae30\uc11c \uc124\uba85\ud560 \uc218 \uc788\ub294 \ub0b4\uc6a9\uc774 \uc544\ub2c8\ub124\uc694. \uc120\ud615\ub300\uc218\uc5d0\uc11c\ub294 \ub9e4\uc6b0 \uc911\uc694\ud55c(^^) \uc758\ubbf8\ub97c \uac00\uc9c0\uace0 \uc788\ub294\ub370, 1\ucc28\ud568\uc218\uc640 \ubca1\ud130\uc758 \uad00\uacc4\uc5d0\uc11c\uc640, 2\ucc28\ud568\uc218\uc5d0\uc11c \ud070 \uc758\ubbf8\ub97c \uac00\uc9d1\ub2c8\ub2e4. – \uae40\uc601\uc6b1 <\/p>\n

    \n

    -— <\/p>\n","protected":false},"excerpt":{"rendered":"

    \uc9c8\ubb38\uc740 Q: \ub97c \ub9d0\uba38\ub9ac\uc5d0 \ubd99\uc774\uace0 \uc368 \uc8fc\uace0, \ub2f5\uae00\uc740 A:\ub97c \ub9d0\uba38\ub9ac\uc5d0 \ubd99\uc774\uba74 \uc88b\uaca0\ub124\uc694. \ub2f5\uae00\uc740 \ud55c\uc904 \ube44\uc6b0\uace0 \uc0c8 \uc904\uc5d0 \uc2dc\uc791\ud558\uba70 A: \uc55e\uc5d0\ub294 \uacf5\ubc31\uc744 \ub123\uc5b4\uc11c \ub4e4\uc5ec\uc4f0\uae30\uac00 \ub418\uac8c \ud574\uc8fc\uc138\uc694. \ub610 \uae00 \ub9c8\uc9c0\ub9c9\uc5d0\ub294 \uc790\uc2e0\uc758 \uc774\ub984\uc744 \ubd99\uc5ec\uc8fc\uc138\uc694. \uae00\uc744 \uc4f0\ub294 \ubc29\ubc95\uc740 \uba54\ub274 \uac00\uc6b4\ub370 ”’\uace0\uce58\uae30”’\ub97c \ub204\ub974\uace0 \ub098\ud0c0\ub098\ub294 \ud3b8\uc9d1\ucc3d\uc5d0 \uc544\ub798\uc640 \uac19\uc774 \uc785\ub825\ud569\ub2c8\ub2e4. \uc911\uac04 \uc911\uac04\uc5d0 \ubbf8\ub9ac\ubcf4\uae30\ub97c \ud574\ub3c4 \ub418\uace0\uc694, \ub9c8\uc9c0\ub9c9\uc5d0\ub294 \uaf2d \uc800\uc7a5\uc744 \ub20c\ub7ec\uc11c \uc368\ub193\uc740 \uae00\uc774 \uc5c6\uc5b4\uc9c0\uc9c0 … \ub354 \uc77d\uae30<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3838","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"\uae40\uc601\uc6b1","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/ywkim","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3838","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/comments?post=3838"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3838\/revisions"}],"predecessor-version":[{"id":3839,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3838\/revisions\/3839"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3838"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3838"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}