{"id":3840,"date":"2006-09-03T06:35:00","date_gmt":"2006-09-02T21:35:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3840"},"modified":"2021-08-12T12:01:31","modified_gmt":"2021-08-12T03:01:31","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%bc2k4","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2006\/09\/03\/%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%bc2k4\/","title":{"rendered":"\u1109\u1165\u11ab\u1112\u1167\u11bc\u1103\u1162\u1109\u116e\u110c\u1175\u11af\u1106\u116e\u11ab\u1107\u1161\u11bc2k4"},"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

{{{-— Q: \uc9c8\ubb38\uc785\ub2c8\ub2e4(\uae40\uc601\uc6b1) <\/p>\n

A: \ub2f5\uc785\ub2c8\ub2e4(\uae40\uc601\uc6b1) -—}}} \uc640 \uac19\uc774 \uc4f0\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \ubcf4\uc785\ub2c8\ub2e4. <\/p>\n

-— Q: \uc9c8\ubb38\uc785\ub2c8\ub2e4. (\uae40\uc601\uc6b1) <\/p>\n

A: \ub2f5\uc785\ub2c8\ub2e4. (\uae40\uc601\uc6b1) <\/p>\n

-— <\/p>\n

\n

Q: C. 6\ubc88\ubb38\uc81c\ub97c \ud480\uae34\ud480\uc5c8\ub294\ub370 \ub9de\ub294\uc9c0 \uc798 \ubaa8\ub974\uaca0\uc2b5\ub2c8\ub2e4. \ud574\uc124 \uc880 \ubd80\ud0c1\ud569\ub2c8\ub2e4. (\uc591\uae38\uc11d) <\/p>\n

A: \uc774 \ubb38\uc81c\ub294 \uc544\ub9c8 \ubb38\uc81c \ud574\uc11d\uc744 \uc798 \ubabb\ud558\ub294 \uac83 \uac19\uc544\uc694. \ubb38\uc81c\uc758 $ Φ$ \ub294 $ \\mathcal{L}=\\mathcal{L}(U,V)$ \uc5d0\uc11c $ \\mathcal{M}=\\mathcal{M}(m,n)$ \uc73c\ub85c\uc758 \ub300\uc751\uad00\uacc4\uc785\ub2c8\ub2e4\ub9cc, \uc774\uac83\uc740 \ubaa8\ub4e0 $ U,V$ \uc640 \ubaa8\ub4e0 $ m,n$ \uc5d0 \ub300\ud558\uc5ec \uc815\uc758\ub418\ub294 \ub9e4\uc6b0 \uad11\ubc94\uc704\ud55c \uc0ac\uc0c1\uc785\ub2c8\ub2e4. \ub530\ub77c\uc11c \uc774 \ubb38\uc81c\ub294 \uc6b0\uc120 $ Φ$ \uac00 $ \\mathcal{L}=\\mathcal{L}(U,V)$ \ud558\ub098\uc5d0 \ub300\ud558\uc5ec\ub294 \ud574\ub2f9\ud558\ub294 $ \\mathcal{M}=\\mathcal{M}(m,n)$ \uc73c\ub85c\uc758 isomorphism \uc784\uc744 \ubcf4\uc774\ub77c\ub294 \uac83\uc774\uace0, \uadf8 \ub2e4\uc74c\uc5d0\ub294 \ub9c8\uc9c0\ub9c9 \ub4f1\uc2dd\uc758 \ud569\uc131 $ Sˆ T$ \uac00 \uc8fc\uc5b4\uc9c0\ub294 \uacbd\uc6b0\uc5d0\ub294 \uadf8\ub7ec\ud55c \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud568\uc744 \ubcf4\uc774\ub77c\ub294 \uac83\uc785\ub2c8\ub2e4. \uc99d\uba85 \uc790\uccb4\ub294 \uc815\uc758\ub97c \ub530\ub77c \ud558\uba74 \uac04\ub2e8\ud55c \uac83\uc785\ub2c8\ub2e4\ub9cc… –\uae40\uc601\uc6b1 <\/p>\n

-— <\/p>\n

\n

Q: \uae30\ub9d0\uace0\uc0ac\uac00 12\uc6d4 15\uc77c\uc774 \ub9de\ub098\uc694? A: 12\uc6d4 15\uc77c \ub9de\uc2b5\ub2c8\ub2e4. <\/p>\n

\n

-— Q: \uc9c8\ubb38\uc774 \ub450\uac00\uc9c0 \uc788\ub294\ub370\uc694, \uc6b0\uc120 adjoint\uc758 \uc815\uc758\uac00 1\ud559\uae30\ub54c \ubc30\uc6b4 \ucc45\ud558\uad6c \uc774\ubc88\uc5d0 \ubc30\uc6b0\ub294 \ucc45\ud558\uace0 \uac19\uc740\uac74\uc9c0 \ub2e4\ub978\uac74\uc9c0 \uad81\uae08\ud574\uc694. \ub2e4\ub978\uac83 \uac19\uc740\ub370, \ucc45\ub9c8\ub2e4 \uc6a9\uc5b4\ub97c \ub2e4\ub974\uac8c \uc4f0\uae30\ub3c4 \ud558\ub098\uc694?? (conjugate transpose\uc778\uac00..;;;) \uadf8\ub9ac\uace0 \ub610\ud558\ub098\ub294 A-1(inverse)\ub791 A*(adjoint)\ub791 \uc131\uc9c8\uac19\uc740\uac8c \ub9ce\uc774 \ube44\uc2b7\ud55c\ub370 \uc815\ud655\ud788 \ub458\uc758 \ucc28\uc774\uc810\uc774 \ubb54\uc9c0 \uc54c\ub824\uc8fc\uc138\uc694.(\uac15\uacbd\uc544) ”’A”’: \uc6b0\uc120 \uc804\uccb4\ub97c \uc815\ub9ac\ud558\ub294\uac8c \uc88b\uc744 \uac83 \uac19\uc544\uc694. <\/p>\n

    \n
  1. \uc2e4\ud589\ub82c $ A $ \uc5d0\ub294 transpose\uac00 \uc788\uc2b5\ub2c8\ub2e4. $ A^T $ \ub77c\uace0 \uc501\ub2c8\ub2e4. \ubb54\uc9c0 \uc54c\uc9c0\uc694?^^(1\ud559\uae30)<\/li>\n
  2. \ubcf5\uc18c\ud589\ub82c $ B $ \uc5d0\ub294 conjugate transpose\uac00 \uc911\uc694\ud569\ub2c8\ub2e4. $ \\overline{B}^T $ \ub77c\uace0 \uc368\uc57c \ud558\uc9c0\uc694.(2\ud559\uae30)<\/li>\n
  3. \uc2e4, \ubcf5\uc18c \ubaa8\ub450, \uc120\ud615\uc0ac\uc0c1 $ A:X→ U $ \uc5d0 \ub300\ud558\uc5ec\ub294 adjoint $ A’:U’→ X’ $ \uc774 \uc788\uc2b5\ub2c8\ub2e4.(2\ud559\uae30, \uad50\uacfc\uc11c 20\ucabd, \uad50\uacfc\uc11c\uc5d0\uc11c\ub294 transpose\ub77c\uace0 \ubd80\ub985\ub2c8\ub2e4.)<\/li>\n
  4. \uc2e4, \ubcf5\uc18c \ubaa8\ub450, \uc120\ud615\uc0ac\uc0c1 $ A:X→ U $ \uc5d0 \ub300\ud558\uc5ec\ub294 (\uc2e4, \ubcf5\uc18c)\ub0b4\uc801\uc5d0 \ub300\ud55c adjoint $ A^*:U→ X $ \uac00 \uc788\uc2b5\ub2c8\ub2e4\ub9cc, \uad50\uacfc\uc11c\uc5d0\uc11c\ub294 \uc120\ud615\ubcc0\ud658 $ A:X→ X $ \uc5d0 \ub300\ud558\uc5ec \ub0b4\uc801\uc5d0 \ub300\ud55c adjoint $ A^*: X→ X $ \ub97c \uc815\uc758\ud558\uace0 \uc788\uc2b5\ub2c8\ub2e4.(2\ud559\uae30, \uad50\uacfc\uc11c 69\ucabd)<\/li>\n
  5. \ub0b4\uc801\uc5d0 \ub300\ud55c adjoint\ub294 \ubca1\ud130\uacf5\uac04 $ X $ \ub97c \uc774 \ub0b4\uc801\uc5d0 \uc758\ud558\uc5ec $ X’ $ \uc640 1\ub3001 \ub300\uc751\uc744 \uc2dc\ucf1c(\uad50\uacfc\uc11c 66\ucabd, corollary 4′) \uc11c\ub85c \ub3d9\uc77c\ud55c \uacf5\uac04\uc774\ub77c\uace0 \uc0dd\uac01\ud558\uae30\ub85c \ud558\uba74 \uc120\ud615\ubcc0\ud658\uc740 $ A’=A^* $ \uac00 \ub429\ub2c8\ub2e4.(69\ucabd\uc758 \uc815\uc758\uc640 19-20\ucabd\uc758 \uc815\uc758\ub97c \ube44\uad50\ud574 \ubcfc \uac83.)<\/li>\n
  6. \uc2e4\ub0b4\uc801\uc774\ub0d0 \ubcf5\uc18c\ub0b4\uc801\uc774\ub0d0\uc5d0 \ub530\ub77c $ A^* $ \uc758 \ud589\ub82c\ud45c\ud604\uc740 $ A^T $ \ub610\ub294 $ \\overline{A}^T $ \uc73c\ub85c \ub429\ub2c8\ub2e4.<\/li>\n<\/ol>\n

    \uc5ec\uae30\uc5d0 \uc758\ubb38\uc0ac\ud56d\uc774 \uc788\uc73c\uba74 \ub2e4\uc2dc \uc9c8\ubb38\ud558\uc148.^^ <\/p>\n

    \n

    \ucd94\uac00<\/h2>\n
    \n

    \ud55c\uac00\uc9c0 \ube60\ub728\ub838\uad70\uc694. A^{-1} \ub791 A^*\ub294 \uc0ac\uc2e4 \uc815\uc758\uc0c1\uc740 \ubcc4 \uc0c1\uad00\uc774 \uc5c6\ub294 \uac83\uc778\ub370… \uc6b0\ub9ac\uac00 \uc911\uc694\ud558\uac8c \uc0dd\uac01\ud558\ub294 2\ucc28\ud615\uc2dd(2\ucc28\ud568\uc218)\uc774\ub860\uc5d0\uc11c\ub294 \ud2b9\ubcc4\ud788 \ubcc0\uc218\ubcc0\ud658\ud558\ub294\ub370 $ A^{-1}=A^* $ \uc778 \uac83\ub4e4\uc744 \uc4f0\uac8c \ub41c\ub2e4\ub294 \uc0ac\uc2e4\uc774 ”’\ubb34\uc9c0\ubb34\uc9c0”’ \uc911\uc694\ud558\ub2c8\uae4c, \uc774\ub7f0\ubcc0\ud658(=\uc9c1\uad50\ubcc0\ud658,unitary\ubcc0\ud658)\uc778 \uacbd\uc6b0\uc5d0\ub9cc \uc774 \ub450 \uac1c\uac00 \uc77c\uce58\ud55c\ub2e4\ub294 \uad00\uacc4\uac00 \uc0dd\uae41\ub2c8\ub2e4. <\/p>\n

    \n

    -— Q.\uac10\uc0ac\ud569\ub2c8\ub2f9~~ \ub9c9 \uc11e\uc5ec\uc788\uc5c8\ub294\ub370 \uc870\uae08 \uc815\ub9ac\uac00 \ub418\ub124\uc694^^ \uadfc\ub370 \uc6b0\ub9ac\uac00 \uc9c0\uae08 \ubc30\uc6b0\ub294 \ubd80\ubd84\uc740 (6\uc7a5~8\uc7a5\uc815\ub3c4) \uc804\ubd80 \ubcf5\uc18c\ud589\ub82c\uacfc \ubcf5\uc18c\ub0b4\uc801\uc778\uac00\uc694? \uadf8\ub9ac\uad6c p81\uc5d0 Th4(b)\uc815\ub9ac\uc788\uc796\uc544\uc694.. \uadf8\uac8c genuine\uc784\uc744 \uc99d\uba85\ud558\uae30 \uc704\ud574\uc11c genralized\ub77c\uace0 \uac00\uc815\ud55c\ub2e4\uc74c\uc5d0 \uadf8\uac8c \uacb0\uad6d genuine\uc784\uc744 \ubcf4\uc778\ub2e4\ub294\uac74 \uc54c\uaca0\ub294\ub370\uc694, induction\uc744 \uc4f8\ub54c d=1\uae4c\uc9c0\ub9cc \uc774\ud574\uac00 \uac00\uc694;; \uadf8\ub2c8\uae4c d=2,3 \uc774\ub807\uac8c \uac00\uba74\uc11c \ubb50\uac00 \uc5b4\ucc0c\ub418\ub294\uac74\uc9c0 \uc798 \ubaa8\ub974\uaca0\uc5b4\uc694. \ub300\ub7b5\uc801 idea\ub9cc \uc0b4\uc9dd \uc124\uba85\ud574\uc8fc\uc138\uc694^^; (\uac15\uacbd\uc544) <\/p>\n

    ”’A”’: \uc6b0\uc120 \uc77c\ubc18 \uc774\ub860\uc740 \ubcf5\uc18c\uacf5\uac04\uacfc \ubcf5\uc18c\ubcc0\ud658, \ubcf5\uc18c\ud589\ub82c\uc785\ub2c8\ub2e4. \ud558\uc9c0\ub9cc \uc77c\ubd80 \uc815\ub9ac\ub294 \uc774\ub7ec\ud55c \ubcf5\uc18c\uc774\ub860\uc744 \uc4f0\uba74 \uc2e4\ubcc0\ud658(\uc2e4\ud589\ub82c)\uc758 \uacbd\uc6b0\uc5d0\ub294 \uc774\ub7ec\uc774\ub7ec\ud558\uac8c \ub41c\ub2e4 \ub77c\uace0 \ud558\uace0 \uc788\uc9c0\uc694. \ub300\ud45c\uc801\uc73c\ub85c \uc2e4\ub300\uce6d\ud589\ub82c\uc758 \uacbd\uc6b0\uc640 \uc774\ub97c \uc774\uc6a9\ud55c \uc2e4 \uc774\ucc28\ud615\uc2dd\uc758 \uacbd\uc6b0\uc785\ub2c8\ub2e4. \uc815\ub9ac4(b)\ub294 \uc6b0\uc120 d=1\uc77c \ub54c\uae4c\uc9c0 \ub410\ub2e4\uace0 \ud558\uace0, … , \uc77c\ubc18\uc801\uc73c\ub85c $ d-1 $ \uae4c\uc9c0 \uc131\ub9bd\ud55c\ub2e4\uace0 \uac00\uc815\ud558\uace0 $ d $ \uc778 \uacbd\uc6b0\ub97c \ubcf4\uc9c0\uc694. (\ucc38\uace0\ub85c \ucc45\uc758 $ H $ \ub294 \uc2e4\uc81c\ub85c $ H-aI $ \uc785\ub2c8\ub2f9.^^) \uc774\uc81c generalized eigenvector \ub77c\ub294 \uc0ac\uc2e4\ub9cc \uc54c\uc544\uc11c $ H^dz=0 $ \ub97c \ub9cc\uc871\uc2dc\ud0a8\ub2e4\uace0 \ud558\uba74 <\/p>\n

    \\[ 0=\\langle H^{d-2}z, H^dz\\rangle = \\langle H^{d-2}z,H^2H^{d-2}z\\rangle \\] \\[ = \\langle HH^{d-2}z,HH^{d-2}z\\rangle = \\langle H^{d-1}z,H^{d-1}z\\rangle = \\| H^{d-1}z\\|^2 \\] <\/p>\n

    (\ub2e4\uc74c\uacfc \uac19\uc774 \uc4f0\ub294\uac8c \ub354 \ub0ab\uaca0\uc9c0\uc694.) \\[ 0=\\langle H^{d-2}z, H^dz\\rangle = \\langle H^{d-2}z,HH^{d-1}z\\rangle \\] \\[= \\langle HH^{d-2}z,H^{d-1}z\\rangle = \\langle H^{d-1}z,H^{d-1}z\\rangle = \\| H^{d-1}z\\|^2 \\] <\/p>\n

    \uc774\ubbc0\ub85c $ H^{d-1}z=0 $ \uc774\ub77c\ub294 \uac83\uc785\ub2c8\ub2e4. \ub530\ub77c\uc11c ( $ d-1 $ \uae4c\uc9c0 \uc131\ub9bd\ud558\ub2c8\uae4c), $ Hz=0 $ \uc774 \ub418\uc5b4 genuin eigenvector\ub77c\ub294 \uac83\uc774\uc9c0\uc694. <\/p>\n<\/div>\n<\/div>\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-3840","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\/3840","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=3840"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3840\/revisions"}],"predecessor-version":[{"id":3841,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3840\/revisions\/3841"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3840"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3840"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}