{"id":3856,"date":"2004-12-06T12:06:00","date_gmt":"2004-12-06T03:06:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3856"},"modified":"2021-08-12T12:01:45","modified_gmt":"2021-08-12T03:01:45","slug":"%e1%84%91%e1%85%ae%e1%86%af%e1%84%8b%e1%85%b53","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2004\/12\/06\/%e1%84%91%e1%85%ae%e1%86%af%e1%84%8b%e1%85%b53\/","title":{"rendered":"\u1111\u116e\u11af\u110b\u11753"},"content":{"rendered":"

= \ud480\uc774 3 =<\/code> <\/p>\n

\n

C.1 \ubc88<\/h2>\n
\n

\uc774 \ubb38\uc81c\uc5d0\ub294 \uc120\ud615\ubcc0\ud658 $A,B$\uac00 \uc815\uc758\ub418\uc5b4 \uc788\ub294 \ubca1\ud130\uacf5\uac04\uc5d0 \ub300\ud55c \uc5b8\uae09\uc774 \uc5c6\ub2e4. \uc774 \ubca1\ud130\uacf5\uac04\uc774 \uc720\ud55c\ucc28\uc6d0 \uacf5\uac04\uc774\ub77c\ub294 \uc870\uac74\uc774 \uc5c6\uc73c\ubbc0\ub85c \uc774 \ubcc0\ud658\uc744 \ud589\ub82c\ub85c \ubc14\uafb8\uc5b4 \uc4f8 \uc218\ub3c4 \uc5c6\uace0, rank\ub098 determinant\ub97c \uc4f8 \uc218\ub3c4 \uc5c6\ub2e4. \ud560 \uc218 \uc5c6\uc774 invertible\uc758 \uc815\uc758\ub098 \uc774\uc640 \ub3d9\uce58\uc778 isomorphism\uc774\ub77c\ub294 \uc0ac\uc2e4\uc744 \ubcf4\uc778\ub2e4. <\/p>\n

\uc989, (\\(\\Rightarrow\\))\ub294 \uac04\ub2e8\ud788 \\((B^{-1}A^{-1})(AB)=Id\\) \uc784\uc744 \ud655\uc778\ud558\ub294 \uc2dd\uc73c\ub85c \ub05d\ub098\uc9c0\ub9cc, (\ub450 \uac1c\uc529 \ub450 \ubc88 \ud655\uc778\ud574\uc57c \ud568. $AB$\uc640 $BA$\uc5d0 \ub300\ud558\uc5ec \uac01\uac01 \uc88c, \uc6b0\ub85c\\ldots) <\/p>\n

(\\(\\Leftarrow\\))\ub294 $AB$\uc640 $BA$\uac00 one-to-one, onto\ub77c\ub294 \uac00\uc815 \uc544\ub798\uc11c \\(A\\), $B$\uac00 \uac01\uac01 one-to-one, onto\uc784\uc744 \ubcf4\uc778\ub2e4. <\/p>\n

(\\(A\\) is one-to-one): $Ax=Ay$\ub77c \ud558\uc790. \uadf8\ub7ec\uba74 $BAx=BAy$\uc774\ub2e4. $BA$\uac00 one-to-one\uc774\ubbc0\ub85c $x=y$\uc774\ub2e4. <\/p>\n

(\\(A\\) is onto): \uc784\uc758\uc758 $z$\uc5d0 \ub300\ud558\uc5ec $AB$\uac00 onto \uc774\ubbc0\ub85c $z=ABy$\uc778 $y$\uac00 \uc874\uc7ac\ud55c\ub2e4. $x=By$\ub77c \ud558\uba74 \uc774 \ubca1\ud130\uc5d0 \ub300\ud558\uc5ec $z=Ax$\uac00 \ub41c\ub2e4. \ub530\ub77c\uc11c $z$\ub294 $A$\uc758 range\uc5d0 \ud3ec\ud568\ub41c\ub2e4. \uc989 $A$\ub294 onto \uc774\ub2e4. <\/p>\n<\/div>\n<\/div>\n

\n

C.2 \ubc88<\/h2>\n
\n

\uc774 \ubb38\uc81c\uc5d0\uc11c\ub294 \ubca1\ud130\uacf5\uac04\uc774 \uc720\ud55c\ucc28\uc6d0\uc774\ub77c\ub294 \uac00\uc815\uc744 \ud558\uace0 \uc788\uace0, \uc774 \ub54c\ub294 \\(AB\\) \ud558\ub098\ub9cc $I$\uc784\uc744 \uc54c\uc544\ub3c4 \ucda9\ubd84\ud558\uba70, $BA$\uc5d0 \ub300\ud55c \uac00\uc815\uc744 \ud558\uc9c0 \uc54a\uc544\ub3c4 $A,B$\uac00 \uac01\uac01 invertible\uc784\uc744 \ubcf4\uc77c \uc218 \uc788\ub2e4. \uc774\ub97c \uc704\ud558\uc5ec\ub294 \ucc28\uc6d0\uc774 \uad00\ub828\ub41c \uac1c\ub150\uc744 \uc368\uc57c \ud55c\ub2e4.(\uc65c? \uc774\ub7f0 \uac1c\ub150\uc774 \uc5c6\uc774 \uc99d\uba85\ub41c\ub2e4\uba74 \uc774 \uc99d\uba85\uc740 \uadf8\ub300\ub85c \uc704\uc758 \ubb38\uc81c\uc5d0 \uc0ac\uc6a9\ub420 \uc218 \uc788\uc744 \uac83\uc774\uace0, \uc704\uc758 \ubb38\uc81c\ub3c4 $AB$\ub9cc invertible\uc784\uc744 \uac00\uc815\ud558\uace0 \uc99d\uba85 \uac00\ub2a5\ud574\uc57c \ud560 \uac83\uc774\uae30 \ub54c\ubb38\uc774\ub2e4.) \\\\[5mm] \uc0ac\uc6a9\ud560 \uc218 \uc788\ub294 \uac1c\ub150\uc740 rank \ub4f1 \ub9ce\uc774 \uc788\uaca0\uc9c0\ub9cc \uc774 \ubb38\uc81c\uc5d0\uc11c \uac00\uc7a5 \uac04\ud3b8\ud55c \uac83\uc740 determinant\uc774\ub2e4. basis\ub97c \ud558\ub098 \uace0\uc815\ud558\uba74 $1=det(AB)=det(A)det(B)$\uc774\ubbc0\ub85c $det(A)≠0$\uc774\ub2e4. \ub530\ub77c\uc11c $A$\ub294 invertible\uc774\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c $B$\ub3c4 invertible\uc774\ub2e4. <\/p>\n<\/div>\n<\/div>\n

\n

C.3 \ubc88<\/h2>\n
\n

$A$\ub294 \ub2e8 \ud558\ub098\ub9cc\uc758 right inverse $B$\ub97c \uac00\uc9c4\ub2e4\uace0 \ud558\ubbc0\ub85c \\(AB=I\\) \uc774\ub2e4. \uc774\uc81c \ud78c\ud2b8\uc758 $BA+B-I$\ub97c $A$\uc758 \uc624\ub978\ucabd\uc5d0 \uacf1\ud574 \ubcf4\uba74, \\[ A(BA+B-I)=ABA+AB-A=IA+I-A=I \\] \uc774\ub2e4. \ub530\ub77c\uc11c \\(BA+B-I\\) \ub3c4 $A$\uc758 right inverse\uc774\ub2e4. \uadf8\ub7f0\ub370 $A$\uc758 right inverse\ub294 \ub2e8 \ud558\ub098\ubfd0\uc774\ub77c\uace0 \ud588\uc73c\ubbc0\ub85c \\(BA+B-I=B\\) \uc774\ub2e4. \uc989 \\(BA=I\\) \uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c $B$\ub294 $A$\uc758 left inverse\uc774\uae30\ub3c4 \ud558\ub2e4. \uc989 $B$\ub294 $A$\uc758 inverse\uac00 \ub418\uace0 $A$\ub294 invertible\uc774\ub2e4. <\/p>\n<\/div>\n<\/div>\n

\n

C.4 \ubc88<\/h2>\n
\n

\uc9c1\uc811 \uacc4\uc0b0\ud574\uc11c \ud655\uc778\ud574 \ubcfc \uac83. <\/p>\n<\/div>\n<\/div>\n

\n

C.5 \ubc88<\/h2>\n
\n

\uc870\uad50 \uc120\uc0dd\ub2d8\uc758 \ub2f5\uc774 \uc633\uc74c. \ub2e8\uc9c0 (1)\uc758 \uc99d\uba85\uc5d0\uc11c \uc2dc\uc791\ubd80\ubd84\uc5d0 $ u_1≠ u_2 $ \ub77c\ub294 \uac00\uc815\uc740 \uc548 \ud558\ub294 \uac83\uc774 \uc633\ub2e4. <\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

= \ud480\uc774 3 = C.1 \ubc88 \uc774 \ubb38\uc81c\uc5d0\ub294 \uc120\ud615\ubcc0\ud658 $A,B$\uac00 \uc815\uc758\ub418\uc5b4 \uc788\ub294 \ubca1\ud130\uacf5\uac04\uc5d0 \ub300\ud55c \uc5b8\uae09\uc774 \uc5c6\ub2e4. \uc774 \ubca1\ud130\uacf5\uac04\uc774 \uc720\ud55c\ucc28\uc6d0 \uacf5\uac04\uc774\ub77c\ub294 \uc870\uac74\uc774 \uc5c6\uc73c\ubbc0\ub85c \uc774 \ubcc0\ud658\uc744 \ud589\ub82c\ub85c \ubc14\uafb8\uc5b4 \uc4f8 \uc218\ub3c4 \uc5c6\uace0, rank\ub098 determinant\ub97c \uc4f8 \uc218\ub3c4 \uc5c6\ub2e4. \ud560 \uc218 \uc5c6\uc774 invertible\uc758 \uc815\uc758\ub098 \uc774\uc640 \ub3d9\uce58\uc778 isomorphism\uc774\ub77c\ub294 \uc0ac\uc2e4\uc744 \ubcf4\uc778\ub2e4. \uc989, (\\(\\Rightarrow\\))\ub294 \uac04\ub2e8\ud788 \\((B^{-1}A^{-1})(AB)=Id\\) \uc784\uc744 \ud655\uc778\ud558\ub294 \uc2dd\uc73c\ub85c \ub05d\ub098\uc9c0\ub9cc, (\ub450 \uac1c\uc529 \ub450 … \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-3856","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\/3856","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=3856"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3856\/revisions"}],"predecessor-version":[{"id":3857,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3856\/revisions\/3857"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3856"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3856"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3856"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}