{"id":9272,"date":"2010-10-09T14:07:00","date_gmt":"2010-10-09T14:07:00","guid":{"rendered":"http:\/\/melotopia.net\/b\/?p=9272"},"modified":"2010-10-09T14:07:00","modified_gmt":"2010-10-09T14:07:00","slug":"%ec%a0%95%ec%9d%98%ec%97%ad-%ec%b9%98%ec%97%ad","status":"publish","type":"post","link":"http:\/\/melotopia.net\/b\/?p=9272","title":{"rendered":"\uc815\uc758\uc5ed, \uce58\uc5ed"},"content":{"rendered":"
\n \uc774\ub7f0 \uba85\uc81c\ub97c \uc0dd\uac01\ud574 \ubcf4\uc790. \uc120\ud615\ub300\uc218\ud559 \ubd84\uc57c\uc774\ub2e4.
\n <\/p>\n
\n L:V->W \uc77c\ub54c,
\n
\n dim(im(L)) == Rank of L\n <\/div>\n

\n \uc774\uac74 \ucc38\uc778\uac00?
\n
\n \uc5ec\uae30\uc11c dim(A)\ub294 A\uc758 \ucc28\uc6d0\uc774\uace0, im(A)\ub294 A\uc758 \uc774\ubbf8\uc9c0 \uacf5\uac04(\uce58\uc5ed)\uc774\ub2e4.<\/p>\n

V\uac00 5\ucc28\uc6d0\uc774\uace0, L\uc758 rank\uac00 5\uc774\uace0 W\uac00 5\ucc28\uc6d0\uc774\uba74 \uc704\uc758 \uba85\uc81c\uac00 \ucc38\uc774 \ub418\ub294 \uc0ac\ub840\uc911\uc758 \ud558\ub098\uc774\ub2e4.
\n
\n V\uac00 3\ucc28\uc6d0\uc774\uace0, L\uc758 rank\uac00 5\uc774\uace0, W\uac00 5\ucc28\uc6d0\uc774\uba74, \uc704\uc758 \uba85\uc81c\uac00 \uac70\uc9d3\uc774 \ub41c\ub2e4. dim(im(L)=3\uc774\uace0 Rank of L=5\uc774\ub2e4.
\n
\n V\uac00 5\ucc28\uc6d0\uc774\uace0, L\uc758 rank\uac00 3\uc774\uace0, W\uac00 5\ucc28\uc6d0\uc774\uba74, \uc704\uc758 \uba85\uc81c\uac00 \ucc38\uc774 \ub41c\ub2e4. dim(im(L))=3\uc774\uace0 Rank of L=3\uc774\ub2e4.<\/p>\n

L\uc758 Rank\ub77c\ub294 \uac1c\ub150\uc744 \uc5b4\ub5bb\uac8c \uc774\ud574\ud574\uc57c\ud558\ub098?<\/p>\n

Rank\ub294 L\uc774\ub77c\ub294 \uc5f0\uc0b0\uc790\uac00 \uac16\uace0 \uc788\ub294 \ud589\uacf5\uac04, \ub610\ub294 \uc5f4\uacf5\uac04\uc758 \ucc28\uc6d0\uc774\ub2e4. \ub9cc\uc57d \ud589\ub82c\uc744 \ud589\ubca1\ud130\ub098 \uc5f4\ubca1\ud130\ub85c \ubd84\ud574\ud574\uc11c \ubcf8\ub2e4\uba74, \uc5b4\ub5a4 \ubca1\ud130 \uacf5\uac04\uc5d0 \uc5f0\uc0b0\uc790\ub97c \uc801\uc6a9\ud55c\ub2e4\ub294 \uac83\uc740 \ud589\ub82c\uc758 \ud589\ubca1\ud130\uc640 \ub0b4\uc801\uc744 \ucde8\ud574\uc11c \uadf8 \uac01\uac01\uc758 \uac12\uc744 \uc0c8\ub85c\uc6b4 \uacf5\uac04\uc758 \uc131\ubd84\uc73c\ub85c \ubcf8\ub2e4\ub294 \ub73b\uc774\ub2e4. \ub530\ub77c\uc11c, \uc5f0\uc0b0\uc790\uc758 \uc801\uc6a9\uc740 \uc8fc\uc5b4\uc9c4 \ubca1\ud130 \uacf5\uac04\uc758 \ubca1\ud130\ub97c \ud589\ubca1\ud130\uac00 \ud45c\ud604\ud558\ub294 \uacf5\uac04\uc73c\ub85c \uc0ac\uc601\uc2dc\ud0a8\ub2e4\ub294 \uac83\uc73c\ub85c \uc0dd\uac01\ud574\ub3c4 \ubb34\ubc29\ud558\ub2e4. \uacf5\uc5ed\uc740 \ub2e8\uc9c0 \uc5f0\uc0b0\uc790\uc5d0 \uc801\uc6a9\ub41c \ud6c4 \uc2e4\uc81c\ub85c \uc0ac\uc6a9\ud558\uae30 \uc704\ud574 \ubca1\ud130\ub97c \ud45c\ud604\ud558\uae30 \uc704\ud574 \ub9c8\ub828\ub41c \uacf5\uac04\uc774\ub2e4.<\/p>\n

\uadf8\ub7fc, \uc704\uc758 \uba85\uc81c\uac00 \ucc38\uc774 \ub418\uae30 \uc704\ud574\uc11c \uc5b4\ub5a4 \uc870\uac74\uc774 \ud544\uc694\ud55c\uac00?
\n
\n \uc6b0\uc120 dim(V)=n, dim(W)=m, Rank(L)=k\ub77c\uace0 \ud558\uc790.<\/p>\n

im(L)\uc774 \uc5b4\ub5bb\uac8c \ub420\uc9c0 \uc0dd\uac01\ud574 \ubcf4\uba74, \uc77c\ub2e8 dim(im(L))<=m\uc774\ub2e4. \uce58\uc5ed\uc774 \uacf5\uc5ed\ubcf4\ub2e4 \ub354 \ud074 \uc218\ub294 \uc5c6\uae30 \ub54c\ubb38\uc774\ub2e4.(\uce58\uc5ed\uc740 \uacf5\uc5ed\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\ub2e4.)\n
\n \ub458\uc9f8\ub85c, dim(im(L))<=n\uc774\ub2e4. \uce58\uc5ed\uc774 \uc815\uc758\uc5ed\ubcf4\ub2e4 \ub354 \ud070 \ucc28\uc6d0\uc744 \uac00\uc9c8 \uc218 \uc5c6\ub2e4. \uc65c\ub0d0\ud558\uba74, \uc815\uc758\uc5ed\uc758 \uae30\uc800\uac00 \uc5f0\uc0b0\uc790\uc5d0 \uc758\ud574\uc11c \uce58\uc5ed\uc5d0\uc11c\ub3c4 \uae30\uc800\uac00 \ub418\ub294\ub370, \ucc28\uc6d0\uc740 \uae30\uc800 \uc9d1\ud569\uc758 \uc6d0\uc18c\uc758 \uc218\uc774\uae30 \ub54c\ubb38\uc774\ub2e4.\n
\n \uc14b\uc9f8\ub85c, dim(im(L))<=k\uc774\ub2e4. \uc55e\uc5d0\uc11c \uc5b8\uae09\ud588\ub4ef\uc774, \uc5f0\uc0b0\uc790\ub97c \uc801\uc6a9\ud55c\ub2e4\ub294 \uac83\uc740 \uc5f0\uc0b0\uc790\uc758 \ud589\uacf5\uac04\uc5d0 \ubca1\ud130\ub97c \uc0ac\uc601\uc2dc\ud0a8\ub2e4\ub294 \ub73b\uc774\uae30 \ub54c\ubb38\uc5d0, \ud589\uacf5\uac04\uc774 \ud45c\ud604\ud560 \uc218 \uc788\ub294 \ucc28\uc6d0\uc774 \uce58\uc5ed\uc758 \ud55c\uacc4\uc774\ub2e4.\n \n\n\n \uc774\uac8c \ud56d\uc0c1 \ucc38\uc774 \ub418\ub824\uba74…\n
\n \uc77c\ub2e8 n=m=k\uc774\uba74 \ucda9\ubd84\ud558\ub2e4. (\uc99d\uba85\uc740 \uc0dd\ub7b5.)<\/p>\n

\uc774\ubcf4\ub2e4 \uc880 \ub354 \ub290\uc2a8\ud55c \uc870\uac74\uc744 \ucc3e\uc544\ubcf4\uc790
\n
\n n\n n>m, m=k\uc774\ub77c\uace0 \ud574 \ubcf4\uc790. \uadf8\ub7fc L\uc758 \uce58\uc5ed\uc740 k\ucc28\uc6d0\uc774\ubbc0\ub85c \uc870\uac74\uc744 \ub9de\ucd9c \uc218 \uc788\ub2e4.<\/p>\n

n=m, n\n n=m, n>k\uc774\ub77c\uace0 \ud574 \ubcf4\uc790. \uadf8\ub7fc L\uc758 \uce58\uc5ed\uc740 k\ucc28\uc6d0\uc774\ubbc0\ub85c \uc870\uac74\uc744 \ub9de\ucd9c \uc218 \uc788\ub2e4.<\/p>\n

n=k, m\n n=k, m>k\uc774\ub77c\uace0 \ud574 \ubcf4\uc790. \uadf8\ub7fc L\uc758 \uce58\uc5ed\uc740 k\ucc28\uc6d0\uc774\ubbc0\ub85c \uc870\uac74\uc744 \ub9de\ucd9c \uc218 \uc788\ub2e4.<\/p>\n

n\n k\n m\n

\n
\n\"\uc2e0\uace0\"
\n<\/a>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\uc774\ub7f0 \uba85\uc81c\ub97c \uc0dd\uac01\ud574 \ubcf4\uc790. \uc120\ud615\ub300\uc218\ud559 \ubd84\uc57c\uc774\ub2e4. L:V->W \uc77c\ub54c, dim(im(L)) == Rank of L \uc774\uac74 \ucc38\uc778\uac00? \uc5ec\uae30\uc11c dim(A)\ub294 A\uc758 \ucc28\uc6d0\uc774\uace0, im(A)\ub294 A\uc758 \uc774\ubbf8\uc9c0 \uacf5\uac04(\uce58\uc5ed)\uc774\ub2e4. V\uac00 5\ucc28\uc6d0\uc774\uace0, L\uc758 rank\uac00 5\uc774\uace0 W\uac00 5\ucc28\uc6d0\uc774\uba74 \uc704\uc758 \uba85\uc81c\uac00 \ucc38\uc774 \ub418\ub294 \uc0ac\ub840\uc911\uc758 \ud558\ub098\uc774\ub2e4. V\uac00 3\ucc28\uc6d0\uc774\uace0, L\uc758 rank\uac00 5\uc774\uace0, W\uac00 5\ucc28\uc6d0\uc774\uba74, \uc704\uc758 \uba85\uc81c\uac00 \uac70\uc9d3\uc774 \ub41c\ub2e4. dim(im(L)=3\uc774\uace0 Rank of L=5\uc774\ub2e4. V\uac00 5\ucc28\uc6d0\uc774\uace0, L\uc758 rank\uac00 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2],"tags":[],"class_list":["post-9272","post","type-post","status-publish","format-standard","hentry","category-academic"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8o6gA-2py","jetpack-related-posts":[],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/9272","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9272"}],"version-history":[{"count":0,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=\/wp\/v2\/posts\/9272\/revisions"}],"wp:attachment":[{"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9272"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/melotopia.net\/b\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}