{"id":3556,"date":"2004-10-15T12:39:00","date_gmt":"2004-10-15T03:39:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3556"},"modified":"2021-08-12T11:56:45","modified_gmt":"2021-08-12T02:56:45","slug":"lectureone","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2004\/10\/15\/lectureone\/","title":{"rendered":"LectureOne"},"content":{"rendered":"

\uccab\uc9f8 \uc8fc\uc758 \uac15\uc758\ub294 \ub300\ubd80\ubd84 1\ud559\uae30\uc758 \uac15\uc758 \ub0b4\uc6a9\uc744 \ub418\ud480\uc774\ud55c \uac83\uc785\ub2c8\ub2e4. <\/p>\n

(TableOfContents) <\/p>\n

[wiki:\uc120\ud615\ub300\uc218\ub0b4\uc6a9: \uc704\ub85c] <\/p>\n

\n

\uc120\ud615\uacf5\uac04(Linear Spaces)<\/h2>\n
\n<\/div>\n
\n

\uc2a4\uce7c\ub77c\uccb4(Scalar Fields)<\/h3>\n
\n

{\uc8fc\uc5b4\uc9c4 \uc9d1\ud569 $K$\uac00 \uccb4(field)\ub97c \uc774\ub8ec\ub2e4 \ud568\uc740 \uc774 \uc9d1\ud569\uc5d0 \ub367\uc148\uacfc \uacf1\uc148\uc774\ub77c\uace0 \ubd88\ub9ac\ub294 \ub450 \uac1c\uc758 \uc148\ubc95\uc774 \uc815\uc758\ub418\uc5b4 \uc788\uc73c\uba74 \uc774 \uc9d1\ud569\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\uac00 \uc774 \uc148\ubc95\uc5d0 \uad00\ud558\uc5ec \ub2e4\uc74c \uc870\uac74\ub4e4\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4\ub294 \ub73b\uc774\ub2e4.} <\/p>\n

{\ub367\uc148\uc5d0 \uad00\ud558\uc5ec} <\/p>\n

\\begin{enumerate}
\n\\item $k+h=h+k$
\n\\item $k+(h+l)=(k+h)+l$
\n\\item \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc6d0\uc18c $0$\uc774 \uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud55c\ub2e4:
\n\uc784\uc758\uc758 $k$\uc5d0 \ub300\ud558\uc5ec $k+0=k$.
\n\\item \uc784\uc758\uc758 $k$\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc6d0\uc18c $h$\uac00
\n\uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud55c\ub2e4: $k+h=0$ (\uc774\ub7ec\ud55c $h$\ub97c \ubcf4\ud1b5 $-k$\ub85c \ub098\ud0c0\ub0b8\ub2e4.)
\n\\end{enumerate}<\/p>\n

{\uacf1\uc148\uc5d0 \uad00\ud558\uc5ec} <\/p>\n

\\begin{enumerate}
\n\\item $kh=hk$
\n\\item $k(hl)=(kh)l$
\n\\item \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc6d0\uc18c $1$\uc774 \uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud55c\ub2e4:
\n$1\\neq0$\uc774\uba70,
\n\uc784\uc758\uc758 $k$\uc5d0 \ub300\ud558\uc5ec $k1=k$.
\n\\item \uc784\uc758\uc758 $0$\uc774 \uc544\ub2cc $k$\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc6d0\uc18c $h$\uac00
\n\uc720\uc77c\ud558\uac8c \uc874\uc7ac\ud55c\ub2e4: $kh=1$ (\uc774\ub7ec\ud55c $h$\ub97c \ubcf4\ud1b5 $k^{-1}$ \ub610\ub294
\n$\\dfrac1k$\ub85c \ub098\ud0c0\ub0b8\ub2e4.)
\n\\end{enumerate}<\/p>\n

\ub367\uc148\uacfc \uacf1\uc148\uc758 \uad00\uacc4\uc5d0 \ub300\ud558\uc5ec <\/p>\n

\\begin{enumerate}
\n\\item $k(h+l)=kh+kl$
\n\\end{enumerate}\n<\/p><\/div>\n<\/div>\n

\n

\uc120\ud615\uacf5\uac04\uc758 \uc815\uc758<\/h3>\n<\/div>\n
\n

\ub3d9\ud615\uc0ac\uc0c1(isomorphism)\uc758 \uac1c\ub150<\/h3>\n
\n

\ub450 \uc120\ud615\uacf5\uac04\uc5d0 \ub300\ud558\uc5ec \uc774 \ub450 \uc120\ud615\uacf5\uac04\uc774 \uadf8 \uc148\ubc95\uc758 \ubaa8\uc591(?)\uc744 \ubcfc \ub54c \ub611 \uac19\uc740 \ubaa8\uc591\uc744 \ud558\uace0 \uc788\ub2e4\uace0 \ub9d0\ud558\uace0 \uc2f6\uc744 \ub54c\uac00 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4 2\ucc28 \ub2e4\ud56d\uc2dd \uc804\uccb4\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc120\ud615\uacf5\uac04\uacfc 3\ucc28\uc6d0 \uc720\ud074\ub9ac\ub4dc\uacf5\uac04 $ \\mathbb{R}^3$ \ub97c \uc0dd\uac01\ud558\uc5ec \ubcf4\uc790. \uc774 \ub54c \ub2e4\ud56d\uc2dd $ ax^2+bx+c$ \uc5d0\uc11c \uacc4\uc218\ub9cc\uc744 \ubf51\uc544 $ (a,b,c)$ \ub97c \ub9cc\ub4e4\uc5b4 \ubcf4\uba74 \uc774 \ub2e4\ud56d\uc2dd\uc5d0 3\ucc28\uc6d0 \ubca1\ud130\ub97c \ud558\ub098 \ub300\uc751\uc2dc\ud0a8 \uac83\uc774 \ub41c\ub2e4. \uc774\uac83\uc740 \ubb3c\ub860 \uc798 \uc815\uc758\ub41c \ud568\uc218\uc774\ub2e4. \uc774 \ud568\uc218\uc758 \uc815\uc758\uc5ed\uc740 2\ucc28\ub2e4\ud56d\uc2dd \uc804\uccb4\uc758 \uacf5\uac04\uc774\uace0, \uacf5\ubcc0\uc5ed\uc740 3\ucc28\uc6d0 \uc720\ud074\ub9ac\ub4dc \uacf5\uac04\uc774\ub2e4. \uc774 \ub54c \uc774 \ub300\uc751\uc740 \ub9e4\uc6b0 \uc790\uc5f0\uc2a4\ub7ec\uc6b8 \ubfd0\ub9cc \uc544\ub2c8\ub77c \uc798 \uc0b4\ud3b4\ubcf4\uba74 \uc774 \ub300\uc751\uc774 1\ub3001 \ub300\uc751\uad00\uacc4\ub97c \uc774\ub8ec\ub2e4\ub294 \uac83\uc744 \uc27d\uac8c \uc54c\uc544\ubcfc \uc218 \uc788\ub2e4. \uc774\uc5d0\uc11c \ub098\uc544\uac00\uc11c \ub2f9\uc5f0\ud55c \uc0ac\uc2e4 \ub610 \ud558\ub098\ub294 \ub2e4\ud56d\uc2dd\uc758 \ub367\uc148\uacfc \uadf8 \uacc4\uc218\ub85c \uc774\ub8e8\uc5b4\uc9c4 3\ucc28\uc6d0 \ubca1\ud130\uc758 \ub367\uc148\uc774 \uc815\ud655\ud788 \uc77c\uce58\ud55c\ub2e4\ub294 \uac83\uc774\ub2e4. \uc989, \\[ (ax^2+bx+c)+(a’x^2+b’x+c’) = (a+a’)x^2+(b+b’)x+(c+c’) \\] <\/p>\n

\\[ (a,b,c)+(a’,b’,c’)=(a+a’,b+b’,c+c’)\\] \uc774\uac83\uc740 \ub204\uad6c\ub098 \uc54c\uace0 \uc788\ub294 \uac83\uc774\uc9c0\ub9cc \ud2b9\ubcc4\ud788 \uc9d1\uc5b4\uc11c \uc774\uc57c\uae30\ud558\uc9c0 \uc54a\uc558\uc5c8\ub2e4. \uc774 \uc0ac\uc2e4\uacfc \ud568\uaed8 \ub610 \ud558\ub098\uc758 \ub2f9\uc5f0\ud55c \uc0ac\uc2e4 \\[ k(ax^2+bx+c)= (ka)x^2+(kb)x+(kc) \\] <\/p>\n

\\[ k(a,b,c)=(ka,kb,kc) \\] \uc744 \ud568\uaed8 \ub193\uc73c\uba74 \uc774\uac83\uc740 \uc704\uc758 1\ub3001 \ub300\uc751\uad00\uacc4\uac00 \uc120\ud615\uc0ac\uc0c1\uc774\ub77c\ub294 \ub9d0\uc774 \ub41c\ub2e4. 1\ub3001 \ub300\uc751\uad00\uacc4\uc5d0\uc11c \uc120\ud615\uc0ac\uc0c1\uc774\ub77c\ub294 \ub9d0\uc740 \uc774 \ub300\uc751\uc744 \ud1b5\ud558\uc5ec \ubcf4\uba74 \ub450 \uc120\ud615\uacf5\uac04\uc758 \ub367\uc148\uacfc \uc2a4\uce7c\ub77c\ubc30\uac00 \uc815\ud655\ud788 \uc77c\uce58\ud55c\ub2e4\ub294 \ub9d0\uc774 \ub41c\ub2e4.(\uc74c\ubbf8\ud558\uc5ec \ubcf4\uc790.) \ub530\ub77c\uc11c \ub450 \uc120\ud615\uacf5\uac04 \uc0ac\uc774\uc758 1\ub3001 \ub300\uc751\uad00\uacc4\uc778 \uc120\ud615\uc0ac\uc0c1\uc740 \ub450 \uacf5\uac04\uc758 \ubaa8\uc591\uc774 \ub611 \uac19\ub2e4(\ub3d9\ud615\uc774\ub2e4)\ub294 \ub73b\uc744 \uac00\uc9c4\ub2e4. \uadf8\ub798\uc11c \uc774\ub7ec\ud55c \uc0ac\uc0c1\uc744 \ub3d9\ud615\uc0ac\uc0c1(isomorphism)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc218\ud559\uc5d0\uc11c \uacf5\ubd80\ud558\ub294 \ubaa8\ub4e0 \uad6c\uc870\uc5d0\uc11c\ub294 \uc11c\ub85c \ub2ec\ub77c\ubcf4\uc774\uc9c0\ub9cc \ub0b4\ub9c9\uc740 \ub611\uac19\uc744 \ub54c \uc0ac\uc6a9\ud558\ub294 \ub3d9\ud615\uc0ac\uc0c1\uc774 \uac00\uc7a5 \uc911\uc694\ud55c \uac1c\ub150 \uac00\uc6b4\ub370 \ud558\ub098\uc774\ub2e4. <\/p>\n<\/div>\n<\/div>\n<\/div>\n

\n

\uc77c\ucc28\ub3c5\ub9bd, \uc885\uc18d<\/h2>\n
\n<\/div>\n
\n

\uc120\ud615\uacb0\ud569(Linear Combination)<\/h3>\n<\/div>\n
\n

\uc77c\ucc28\uc885\uc18d\uc131(Linear Dependence)<\/h3>\n<\/div>\n
\n

\ubc14\ud0d5\ubca1\ud130(Basis)<\/h3>\n<\/div>\n<\/div>\n
\n

Quotient Spaces : 2\ud559\uae30\uc758 \uc0c8\ub85c\uc6b4 \uc5bc\uad74<\/h2>\n
\n

[wiki:\uc120\ud615\ub300\uc218\ub0b4\uc6a9: \uc704\ub85c] <\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\uccab\uc9f8 \uc8fc\uc758 \uac15\uc758\ub294 \ub300\ubd80\ubd84 1\ud559\uae30\uc758 \uac15\uc758 \ub0b4\uc6a9\uc744 \ub418\ud480\uc774\ud55c \uac83\uc785\ub2c8\ub2e4. (TableOfContents) [wiki:\uc120\ud615\ub300\uc218\ub0b4\uc6a9: \uc704\ub85c] \uc120\ud615\uacf5\uac04(Linear Spaces) \uc2a4\uce7c\ub77c\uccb4(Scalar Fields) {\uc8fc\uc5b4\uc9c4 \uc9d1\ud569 $K$\uac00 \uccb4(field)\ub97c \uc774\ub8ec\ub2e4 \ud568\uc740 \uc774 \uc9d1\ud569\uc5d0 \ub367\uc148\uacfc \uacf1\uc148\uc774\ub77c\uace0 \ubd88\ub9ac\ub294 \ub450 \uac1c\uc758 \uc148\ubc95\uc774 \uc815\uc758\ub418\uc5b4 \uc788\uc73c\uba74 \uc774 \uc9d1\ud569\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\uac00 \uc774 \uc148\ubc95\uc5d0 \uad00\ud558\uc5ec \ub2e4\uc74c \uc870\uac74\ub4e4\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4\ub294 \ub73b\uc774\ub2e4.} {\ub367\uc148\uc5d0 \uad00\ud558\uc5ec} \\begin{enumerate} \\item $k+h=h+k$ \\item $k+(h+l)=(k+h)+l$ \\item \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc6d0\uc18c … \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-3556","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\/3556","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=3556"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3556\/revisions"}],"predecessor-version":[{"id":3557,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3556\/revisions\/3557"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3556"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3556"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3556"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}