(TableOfContents) <\/p>\n
\uc9c1\uc811 \uacc4\uc0b0\ud558\uc5ec \ubcf4\uc77c \uac83. <\/p>\n<\/div>\n<\/div>\n
$y$\ub294 \\(V\\) \uc704\uc5d0 \uc815\uc758\ub41cnon-zero linear function \uc774\ubbc0\ub85c \\(p\\in V\\) \uac00 \uc874\uc7ac\ud558\uc5ec \\(y(p)=q\\neq 0\\) \uac00 \ub41c\ub2e4. \uc774\uc81c \uc784\uc758\uc758 \uc2a4\uce7c\ub77c $α$\uc5d0 \ub300\ud558\uc5ec \\(\\alpha p\/q\\) \uc5d0\uc11c $y$\uc758 \uac12\uc744 \uacc4\uc0b0\ud558\uc5ec \ubcf4\uba74 \\[ y\\left(\\frac{\\alpha p}q\\right) = \\frac{\\alpha}q y(p) = \\alpha \\] \uc774\ubbc0\ub85c \\(y(x)=\\alpha\\) \uc778 $x=\\dfrac{\\alpha p}q∈ V$\uac00 \uc874\uc7ac\ud55c\ub2e4. (\ubc15\ubc30\uc900\uc758 \ub2f5) <\/p>\n<\/div>\n<\/div>\n
\ub9cc\uc77c \\(z=0\\) \uc774\ub77c\uba74 \ubaa8\ub4e0 $x$\uc5d0 \ub300\ud558\uc5ec $z(x)=0$\uc774\ubbc0\ub85c \ubb38\uc81c\uc758 \uc870\uac74\uc5d0 \uc758\ud558\uc5ec \ubaa8\ub4e0 $x$\uc5d0 \ub300\ud558\uc5ec $y(x)=0$\uc774 \ub418\uc5b4 $y=0$\uc774 \ub418\uace0 \ub530\ub77c\uc11c \ud56d\uc0c1 $y=x$\uac00 \ub41c\ub2e4. \uc989 $α=1$\uc774\uba74 \ub41c\ub2e4. <\/p>\n
\uc774\uc81c $z≠0$\uc774\ub77c\uba74 $z(x_0)≠0$\uc778 $x_0$\uac00 \uc788\ub2e4. \uc774 \ub54c, \ud78c\ud2b8\uc640 \uac19\uc774 \\(\\alpha=y(x_0)\/z(x_0)\\) \ub77c \ub193\uc790. \uc774\uc81c \ubaa8\ub4e0 $x$\uc5d0 \ub300\ud558\uc5ec $y(x)=α z(x)$\uc784\uc744 \ubcf4\uc774\uc790. \\\\[3mm] $x$\ub97c \uc784\uc758\ub85c \uc7a1\uc790. \\[ x= \\frac{z(x)}{z(x_0)}x_0 + x – \\frac{z(x)}{z(x_0)}x_0 \\] \uc774\ubbc0\ub85c \\[ y(x)= \\frac{z(x)}{z(x_0)}y(x_0) + y(x – \\frac{z(x)}{z(x_0)}x_0) = \\alpha z(x) – y(x – \\frac{z(x)}{z(x_0)}x_0) \\] \uc774\ub2e4. <\/p>\n
\ud55c\ud3b8 $ z(x – \\frac{z(x)}{z(x_0)}x_0)=0 $ \uc774\ubbc0\ub85c $ y(x – \\frac{z(x)}{z(x_0)}x_0)=0 $ \uc774\ub2e4. \ub530\ub77c\uc11c \\(y(x)=\\alpha z(x)\\) \uc774\ub2e4. <\/p>\n
(\uc99d\uba85 \ub05d) <\/p>\n<\/div>\n<\/div>\n
$y_i$\ub294 $V$\uc5d0\uc11c $\\mathbb{R}$\ub85c\uc758 1\ucc28\ud568\uc218\uc774\ub2e4. \ub530\ub77c\uc11c $(y_1,…,y_m)$\ub77c\uace0 \uc4f0\uba74 \uc774\uac83\uc740 $V$\uc5d0\uc11c $\\mathbb{R}^m$\uc73c\ub85c\uc758 \uc120\ud615\uc0ac\uc0c1\uc744 \uc815\uc758\ud55c\ub2e4. \uc774 \uc120\ud615\uc0ac\uc0c1\uc744 $S$\ub77c\uace0 \ud558\uc790. <\/p>\n
\uc774\uc81c \ubaa8\ub4e0 \\(i=1,\\dots,m\\) \uc5d0 \ub300\ud558\uc5ec $y_i(x)=α_i$\ub77c \ud568\uc740 \\(S(x)=(\\alpha_1,\\dots,\\alpha_m)\\) \ub77c\ub294 \ub73b\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \ubb38\uc81c\uc5d0\uc11c\uc640 \uac19\uc740 $x$\uac00 \uc874\uc7ac\ud55c\ub2e4\ub294 \ub9d0\uc740 $v=(α_1,…,α_m)$\ub77c\ub294 $\\mathbb{R}^m$\uc758 \ubca1\ud130\uac00 $S$\uc758 range $R_S$\uc5d0 \uc18d\ud55c\ub2e4\ub294 \ub9d0\uacfc \uac19\ub2e4. \uc774\uc81c \uad50\uacfc\uc11c 21\ucabd \uc815\ub9ac $2’$\uc744 \uc0ac\uc6a9\ud558\uba74 \uc774 \ub9d0\uc740 \ubca1\ud130 $v=(α_1,…,α_m)$\uac00 $N_{S’}^{⊥}$\uc5d0 \uc18d\ud55c\ub2e4\ub294 \ub9d0\uacfc \ub3d9\uce58\uc774\ub2e4. \uc774 \ub9d0\uc744 \ud480\uc5b4 \uc368\ubcf4\uc790. <\/p>\n
~ <\/p>\n
\\(v\\in N_{S’}^{\\perp}\\) \\(\\Leftrightarrow\\) <\/p>\n
$∀ l∈ N_{S’}$\uc5d0 \ub300\ud558\uc5ec \\(l(v)=0\\) \\(\\Leftrightarrow\\) <\/p>\n
[ \\(S’l=0\\) \\(\\Rightarrow\\) \\(l(v)=0\\) ] \\(\\Leftrightarrow\\) <\/p>\n
[ [ $∀ z$\uc5d0 \ub300\ud558\uc5ec \\(S’l(z)=l(Sz)=0\\) ] \\(\\Rightarrow\\) \\(l(v)=0\\) ] \\(\\Leftrightarrow\\) <\/p>\n
~ ~ ~ ~ ~ \uc774 \ub9d0\uc744 \ud480\uc5b4\uc4f0\uba74 <\/p>\n
[ \\(S’l=l\\circ S\\) \ub77c\ub294 1\ucc28\ud568\uc218\uac00 \uc0c1\uc218\ud568\uc218 $0$\uc774\uba74 \\(l(v)=0\\) \uc774\ub2e4. ] <\/p>\n
~ <\/p>\n
~ ~ ~ ~ ~ $(\\mathbb{R}^m)’$\uc758 \uc6d0\uc18c\uc778 $\\mathbb{R}^m$\uc758 1\ucc28\ud568\uc218 $l$\uc740 <\/p>\n
~ ~ ~ ~ ~ \\(\\lambda_1k_1+\\cdots+\\lambda_mk_m\\) \uaf34\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\uc73c\ubbc0\ub85c <\/p>\n
~ ~ ~ ~ ~ \\(S’l=l\\circ S=\\lambda_1y_1+\\cdots+\\lambda_my_m\\) \uc774\ub2e4. <\/p>\n
~ ~ ~ ~ ~ \ub530\ub77c\uc11c \uc704\uc758 \ub9d0\uc740 \ub2e4\uc74c\uacfc \ub3d9\uce58\uc774\ub2e4. <\/p>\n
~ <\/p>\n
\\(\\Leftrightarrow\\) [ \\(\\lambda_1y_1+\\cdots+\\lambda_my_m=0\\) \\(\\Rightarrow\\) \\(\\lambda_1\\alpha_1+\\cdots+\\lambda_m\\alpha_m=0\\) ] <\/p>\n
~ <\/p>\n
\uc774\uc81c \uc774\uac83\uc744 \ubc29\uc815\uc2dd\uc5d0 \uc801\uc6a9\ud558\uc5ec \ubcf4\uc790. $y_i(x)=α_i$\ub77c\ub294 \uac83\uc740 1\ucc28\ubc29\uc815\uc2dd\uc774\ub2e4. \ub530\ub77c\uc11c \ubb38\uc81c\ub294 $m$\uac1c\uc758 \ube44\uc81c\ucc28\uc778 $n$\uc6d0 1\ucc28 \uc5f0\ub9bd\ubc29\uc815\uc2dd\uc5d0\uc11c \uc0c1\uc218\ud56d $α_i$\ub4e4\uc5d0 \ub300\ud558\uc5ec \ubc29\uc815\uc2dd\uc758 \ud574\uac00 \uc801\uc5b4\ub3c4 \ud558\ub098 \uc874\uc7ac\ud558\uae30 \uc704\ud55c $α_i$\ub4e4\uc758 \ud544\ucda9\uc870\uac74\uc744 \uad6c\ud558\ub77c\ub294 \uac83\uc774\ub2e4. \uadf8 \ub2f5\uc73c\ub85c \uc5bb\uc740 \uc870\uac74\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4. \uc989, $y_i$\ub4e4\uc774 1\ucc28\uc885\uc18d\uc77c \uacbd\uc6b0\uc5d0\ub9cc \ubb38\uc81c\uac00 \ub418\uba70, \uc774 \uacbd\uc6b0\uc5d0\ub294 $y_i$\uc758 1\ucc28\uacb0\ud569\uc73c\ub85c 0\ud568\uc218\ub97c \ub9cc\ub4e4 \uc218 \uc788\uc744 \ub54c \uc774 1\ucc28\uacb0\ud569\uacfc \ub611 \uac19\uc740 \ubaa8\uc591\uc73c\ub85c $α_i$\uc758 1\ucc28\uacb0\ud569\uc744 \ub9cc\ub4e4\uba74 \uc774\uac83\ub3c4 \ud56d\uc0c1 0\uc774 \ub41c\ub2e4\ub294 \uc870\uac74\uc744 $α_i$\ub4e4\uc774 \ub9cc\uc871\ud558\uc5ec\uc57c\ub9cc \uc774\ub7ec\ud55c \ud574 $x$\uac00 \uc788\ub2e4\ub294 \ub73b\uc774\ub2e4. <\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
(TableOfContents) B.1 \ubc88 \uc9c1\uc811 \uacc4\uc0b0\ud558\uc5ec \ubcf4\uc77c \uac83. B.2 \ubc88 $y$\ub294 \\(V\\) \uc704\uc5d0 \uc815\uc758\ub41cnon-zero linear function \uc774\ubbc0\ub85c \\(p\\in V\\) \uac00 \uc874\uc7ac\ud558\uc5ec \\(y(p)=q\\neq 0\\) \uac00 \ub41c\ub2e4. \uc774\uc81c \uc784\uc758\uc758 \uc2a4\uce7c\ub77c $α$\uc5d0 \ub300\ud558\uc5ec \\(\\alpha p\/q\\) \uc5d0\uc11c $y$\uc758 \uac12\uc744 \uacc4\uc0b0\ud558\uc5ec \ubcf4\uba74 \\[ y\\left(\\frac{\\alpha p}q\\right) = \\frac{\\alpha}q y(p) = \\alpha \\] \uc774\ubbc0\ub85c \\(y(x)=\\alpha\\) \uc778 $x=\\dfrac{\\alpha p}q∈ V$\uac00 \uc874\uc7ac\ud55c\ub2e4. (\ubc15\ubc30\uc900\uc758 \ub2f5) B.3 … \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-3854","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\/3854","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=3854"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3854\/revisions"}],"predecessor-version":[{"id":3855,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3854\/revisions\/3855"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3854"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3854"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3854"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}