{"id":3278,"date":"2011-06-10T14:21:00","date_gmt":"2011-06-10T05:21:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3278"},"modified":"2021-09-02T15:55:09","modified_gmt":"2021-09-02T06:55:09","slug":"%ec%84%a0%ed%98%95%eb%8c%80%ec%88%98-i-2011-%eb%b4%84","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2011\/06\/10\/%ec%84%a0%ed%98%95%eb%8c%80%ec%88%98-i-2011-%eb%b4%84\/","title":{"rendered":"\uc120\ud615\ub300\uc218 I (2011 \ubd04)"},"content":{"rendered":"<div id=\"outline-container-org37e05a5\" class=\"outline-2\">\n<h2 id=\"org37e05a5\">\uacf5\uc9c0\uc0ac\ud56d<\/h2>\n<div class=\"outline-text-2\" id=\"text-org37e05a5\">\n<ul class=\"org-ul\">\n<li>\uc219\uc81c \uc81c\ucd9c\uc740 Exercises section \ud558\ub098\uc529 \uc81c\ucd9c\ud569\ub2c8\ub2e4. &#8221;&#8217;\uc219\uc81c \uc81c\ucd9c \uae30\ud55c\uc740 \uac01 \uc808\uc744 \uc2dc\uc791\ud55c \ub0a0\ub85c\ubd80\ud130 1\uc8fc\uc77c&#8221;&#8217;\uc785\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uba74 1.4\uc808\uc744 \uc6d4\uc694\uc77c\uc5d0 \uc2dc\uc791\ud588\uc73c\uba74 \ub2e4\uc74c \uc8fc \uc6d4\uc694\uc77c &#8221;&#8217;\uac15\uc758\uc2dc\uac04 \uc804\uae4c\uc9c0&#8221;&#8217; 1.4\uc808\uc758 \ubb38\uc81c\ub97c \ud480\uc5b4 \uc81c\ucd9c\ud569\ub2c8\ub2e4. \uc219\uc81c \uc81c\ucd9c\uc740 \uc219\uc81c \uc81c\ucd9c \ubc15\uc2a4\ub97c \uc774\uc6a9\ud569\ub2c8\ub2e4.<\/li>\n<li>\uc219\uc81c: <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/2k11s_LA_exercises.pdf\">2k11s_LA_exercises.pdf<\/a> : \uc774 \ud30c\uc77c\uc740 \uacc4\uc18d\ud574\uc11c \uc5c5\ub370\uc774\ud2b8 \ub429\ub2c8\ub2e4.<\/li>\n<\/ul>\n<p> (UploadFile) <\/p>\n<\/div>\n<\/div>\n<div id=\"outline-container-org27cbc39\" class=\"outline-2\">\n<h2 id=\"org27cbc39\">\uc5f0\uc2b5<\/h2>\n<div class=\"outline-text-2\" id=\"text-org27cbc39\">\n<ul class=\"org-ul\">\n<li>2011\ub144 6\uc6d410\uc77c\uae4c\uc9c0 \uc219\uc81c\ud568\uc5d0 \uc219\uc81c \ub123\uc5b4 \ub450\uaca0\uc2b5\ub2c8\ub2e4. \ucc3e\uc544\uac00\uc138\uc694.<\/li>\n<li>2011\ub144 6\uc6d408\uc77c Least Square solution, Orthogonal Bases and A=QR Factorization.<\/li>\n<li>Gram-Schmidt Process and QR Fatorization <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/gramschmit.txt\">gramschmit.txt<\/a>   (MATLAB)<\/li>\n<li>Orthogonal Vectors and Projections <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/aa7.pdf\">aa7.pdf<\/a><\/li>\n<li>2011\ub144 4\uc6d420\uc77c \uc5f0\uc2b5\ud569\ub2c8\ub2e4.<\/li>\n<li>2011\ub144 4\uc6d413\uc77c \uc5f0\uc2b5 <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/aa6.pdf\">aa6.pdf<\/a><\/li>\n<li>2011\ub144 4\uc6d406\uc77c \uc5f0\uc2b5 <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/aa5.pdf\">aa5.pdf<\/a><\/li>\n<li>2011\ub144 3\uc6d430\uc77c \uc5f0\uc2b5 <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/aa4.pdf\">aa4.pdf<\/a><\/li>\n<li>2011\ub144 3\uc6d423\uc77c \uc5f0\uc2b5 <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/aa3.pdf\">aa3.pdf<\/a><\/li>\n<li>2011\ub144 3\uc6d416\uc77c \uc5f0\uc2b5 <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/maa2.pdf\">maa2.pdf<\/a><\/li>\n<li>2011\ub144 3\uc6d4 9\uc77c \uc5f0\uc2b5 <a href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-content\/uploads\/sites\/8\/attachments\/2k11LinAlgOne\/aa1.pdf\">aa1.pdf<\/a><\/li>\n<li>\uc219\uc81c\ud568\uc740 \uc544\uc0b0\uc774\ud559\uad00 5\uce35 \uc218\ud559\ud1a0\ub860\ubc29 \uc548\ucabd\uc5d0 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"outline-container-org46e180e\" class=\"outline-2\">\n<h2 id=\"org46e180e\">\uc9c8\ubb38<\/h2>\n<div class=\"outline-text-2\" id=\"text-org46e180e\">\n<p> Q. \uc5b4\ub5a4 matrix\uac00 R^2\uc758 \uacf5\uac04\uc758 \uc5b4\ub5a4 \ud3c9\uba74 P\ub97c nullspace\ub85c \ub450\uace0 \uc788\ub2e4\ub294 \uac83\uc774 \ubb34\uc2a8 \uc758\ubbf8\uc778\uac00\uc694? \uc5b4\ub5bb\uac8c \uc774 martix \ub97c \uad6c\ud574\uc57c \ud558\ub294\uc9c0\uc694. \ud5f7\uac08\ub824\uc11c \uc9c8\ubb38\ub4dc\ub9bd\ub2c8\ub2e4.. \uac10\uc0ac\ud569\ub2c8\ub2e4. (\ubb3c\ub9ac\ud559\uacfc 2005160042) <\/p>\n<hr \/>\n<p> Q. 3.3 \uc808\uc5d0\uc11c \uc9c8\ubb38\ub4dc\ub9bd\ub2c8\ub2e4. (\ubb3c\ub9ac\ud559\uacfc 2010160147) A\uac00 independent columns \ub97c \uac00\uc9c0\uba74 A^T A \uac00 square, symmetic, invertible \uc778 \uc774\uc720\uac00 \ubb34\uc5c7\uc778\uac00\uc694? <\/p>\n<p> -&gt; \\[ A \\] \uac00 \\[ (m \\times n) \\] \uc774\ub77c\uba74 \\[ A^T A \\] \ub294 ( \\[ n \\]  by  \\[ m \\] ) times ( \\[ m \\]  by   \\[ n \\] )\uac00 \ub418\uc5b4\uc11c \uadf8 \uacb0\uacfc\ub294 ( \\[ n \\] by \\[ n \\] ) square\uac00 \ub418\uaca0\uc9c0\uc694. \uadf8\ub9ac\uace0  \\[ (A^T A)^T=(A^T A) \\] \uc774\ubbc0\ub85c symmetric\uc785\ub2c8\ub2e4. invertible \uc778 \uc774\uc720\ub294 \\[ A \\] \uc640 \\[ A^T A \\] \uac00 \uac19\uc740 nullspace\ub97c \uac00\uc9c0\uace0 \uc788\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4. \ub2f5\uc774 \ub418\uc5c8\ub098\uc694? <\/p>\n<hr \/>\n<p> Q. 3.3\uc808\uc5d0\uc11c \uc9c8\ubb38\ub4dc\ub9bd\ub2c8\ub2e4. (\ubb3c\ub9ac\ud559\uacfc 2007160095) <\/p>\n<p> 162\ucabd\uc5d0 figure 3.8\uc5d0\uc11c \uc9c8\ubb38\ub4dc\ub9bd\ub2c8\ub2e4. A\uc758 Column space C(A)\uc640 error vector(b-p)\ub294 \uc11c\ub85c orthogonal complement \uc778\uac00\uc694? <\/p>\n<p> \uc6b0\uc120, e\uac00 C(A)\uc758 \ubaa8\ub4e0 vector\ub4e4\uacfc \uc218\uc9c1\ud558\uace0, \ub450 subspace\uc758 dimension\uc744 \ud569\ud558\uba74 \uc804\uccb4 \uacf5\uac04 R^3 \uc774 \ub418\ub2c8\uae4c \uc11c\ub85c orthogonal complement\uac00 \ub418\ub294 \uac83 \uac19\uc740\ub370&#x2026; \uc11c\ub85c orthogonal complement\uc774\ub824\uba74 \ub450 subspace \ubaa8\ub450 0\ubca1\ud130\ub97c \ud3ec\ud568\ud574\uc57c \ud558\uace0, 0\ubca1\ud130\uc5d0\uc11c\ub9cc \ub9cc\ub098\uc57c \ud558\ub294 \uac83 \uc544\ub2cc\uac00\uc694? \uadf8\ub7ec\ud55c \uac83\uc5d0 \ub300\ud55c \uc124\uba85\uc5c6\uc774 orthogonal complement\ub77c\uace0 \ud574\ub3c4 \ub418\ub294\uc9c0&#x2026; (164\ucabd\uc5d0 projection matrix\uc5d0 \ub300\ud55c \uc124\uba85\uc5d0\uc11c\ub3c4 \ub450 \uac1c\uac00 \uc11c\ub85c orthogonal complement\ub77c\uace0 \ub098\uc640\uc788\ub358\ub370&#x2026;) <\/p>\n<p> \uc544; \ub2e4\uc2dc \uc0dd\uac01\ud574\ubcf4\ub2c8\uae4c&#x2026;\ub450 subspace\uc758 \uad50\uc9d1\ud569\uc774 0\ubca1\ud130\ubc16\uc5d0 \uc5c6\ub294\uac8c \ub9de\uad70\uc694&#x2026;\u315c\u315c (\uc810\uc5d0\uc11c \ub9cc\ub098\ub2c8\uae4c) <\/p>\n<p> \uc81c\uac00 0\ubca1\ud130\ub97c(0,0,0)\uc5d0\uc11c \ub9cc\ub098\uc57c\ud55c\ub2e4\ub294 \uac83\uacfc \ud63c\ub3d9\ud588\ub124\uc694&#x2026; <\/p>\n<hr \/>\n<p> Q. rank(AB)\\(\\leq\\) rank(A)\uc774 \uc131\ub9bd\ud558\ub294 \uc774\uc720\ub294? <\/p>\n<p> AB\ub294 column A\uc758 linear combination\uc774\uae30 \ub54c\ubb38\uc785\ub2c8\ub2e4. <\/p>\n<hr \/>\n<p> Q. \ubb3c\ub9ac\ud559\uacfc 2005160016 2.2 \uc808\uc5d0 figure2.2 \uc758 complete solution\uc5d0 \uad00\ud55c \uc9c8\ubb38\uc785\ub2c8\ub2e4. <\/p>\n<p> \uadf8\ub9bc\uc5d0\uc11c\ub294 particular solution\ub450 \uac00\uc9c0\ub97c \ud45c\ud604\ud574 \ub1a8\ub294\ub370 (1,1) \uc740 shortest \uc774\uace0 (2,0) \uc740 \ub9e4\ud2b8\ub7a9\uc758 \uc194\ub8e8\uc158\uc774\ub77c\uace0 \ub418\uc5b4\uc788\uc2b5\ub2c8\ub2e4. \ubcf8\ubb38\uc5d0\uc11c\ub294 \uc774 \uc2dd\uc5d0\uc11c\uc758 complete sol.\uc744 \uad6c\ud558\ub294 \uacfc\uc815\uc5d0\uc11c particular sol. \uc744 (1,1)\ub85c \ud558\uc5ec complete sol.\uc744 (1-c,1+c)\ub77c \ud588\uc2b5\ub2c8\ub2e4. <\/p>\n<p> \uadf8\ub7f0\ub370 \uc774\ub54c particular sol.\uc744 (2,0)\uc73c\ub85c \ud558\uba74 complete sol. \uc774 (2-c, c) \uac00 \ub418\ub294\ub370 \uc774\ub807\uac8c \ud574\ub3c4 \ub9de\ub294\uac74\uac00\uc694? <\/p>\n<p> complete sol.\uc774 \ubc18\ub4dc\uc2dc \ud558\ub098\ub9cc \uc874\uc7ac\ud558\ub294\uac74\uc9c0 \uc544\ub2c8\uba74 \uc774\ub807\uac8c particular sol.\uc758 \uc124\uc815\uc5d0 \ub530\ub77c \ubb34\ud55c\ud788 \ubc14\ub014\uc218 \uc774\ub294\uac74\uc9c0 \ud5f7\uac08\ub9bd\ub2c8\ub2e4&#x2026; <\/p>\n<p> &#8221;&#8217;A&#8221;&#8217;: \uc774 \ub450 solution\uc740 \uac19\uc740 solution\uc785\ub2c8\ub2e4. $ (2-c,c)=(1-(c-1), 1+(c-1))=(1-d,1+d) $ \uc774\ubbc0\ub85c \ub450 \ud45c\ud604\uc774 \ub098\ud0c0\ub0b4\ub294 \ud574 \uc804\uccb4\uc758 \uc9d1\ud569\uc740 \uac19\uc740 \uc9d1\ud569\uc785\ub2c8\ub2e4. \uc6b0\ub9ac\uac00 solution\uc774\ub77c \ud558\uba74 solution\uc758 \ud45c\ud604 \ud615\ud0dc\ub97c \ub9d0\ud558\ub294 \uac83\uc774 \uc544\ub2c8\ub77c solution\uc758 \uc9d1\ud569\uc744 \ub9d0\ud558\ub294 \uac83\uc774\uc9c0\uc694. \uc774\uac83\uc740 \uace0\ub4f1\ud559\uad50\ub54c \ub2e4 \ubc30\uc6b4 \uac83\uc778\ub370&#x2026; \ub300\ubd80\ubd84 \uc815\uc758\ub97c \uae30\uc5b5\ud558\uc9c0 \ubabb\ud558\uc9c0\uc694. \uc774\ub7f0 \uae30\ud68c\uc5d0 \uace0\ub4f1\ud559\uad50\ub54c \uacf5\ubd80\ud55c \uac83\ub4e4\uc744 \ub418\ub3cc\uc544\ubcfc \ud544\uc694\uac00 \uc788\uc5b4\uc694. <\/p>\n<hr \/>\n<p> Q. \uccab \ubc88\uc9f8 \uc9c8\ubb38\uc785\ub2c8\ub2e4. (\ubb3c\ub9ac\ud559\uacfc 2007160095) <\/p>\n<p> 2.4\uc808\uc5d0 Existence of inverses\uc5d0 \uad00\ud574\uc11c \uc9c8\ubb38\ub4dc\ub9bd\ub2c8\ub2e4. <\/p>\n<p> UNIQUENESS: Full column rank r = n. Ax = b has at most one solution x for every b if and only if the columns are linearly independent. Then A has an n by m left-inverse B such that BA = I&#8221;'(n by n)&#8221;&#8217;. This is possible only if m &gt; n. <\/p>\n<p> In the uniqueness case, if there is a solution to &#8221;&#8217;Ax = b&#8221;&#8217;, it has to be x = BAx = Bb. But there may be no solution. The number of solutions is 0 or 1. <\/p>\n<p> \uc5ec\uae30\uc5d0\uc11c, \uc774 uniqueness\uc758 \uacbd\uc6b0\uc5d0\ub294 A\uac00 left-inverse\ub97c \uac16\uc796\uc544\uc694. \uadf8\ub7f0\ub370 \ubc14\ub85c \uc704\uc5d0 \uad75\uac8c \ud45c\uc2dc\ud55c \uc2dd\uc5d0 x \ub300\uc2e0\uc5d0 Bb\ub97c \ub123\uc5b4\ubcf4\uba74, <\/p>\n<p> A(Bb)=b \uc774\uace0, <\/p>\n<p> \uc989, (AB)b=b \uc774\ubbc0\ub85c AB=I&#8221;'(m by m)&#8221;&#8217; \uac00 \ub418\uc5b4, A\ub294 left-inverse \ubfd0\ub9cc \uc544\ub2c8\ub77c right inverse\ub3c4 \uac16\uac8c \ub418\ub294 \uac83 \uc544\ub2cc\uac00\uc694 ?? <\/p>\n<p> \u2192 Ax=b\uc5d0 \uadfc\uc774 \uc5c6\uc744 \uc218\ub3c4 \uc788\uaca0\uc9c0\uc694. <\/p>\n<p> \u2192 \uadf8\ub807\ub2e4\uba74,\uadfc\uc774 \uc788\uc73c\uba74 right inverse\ub3c4 \uac16\uac8c \ub418\ub294 \uac83\uc778\uac00\uc694? <\/p>\n<p> A:  $ ABb=b$ \ub77c\uace0 \ud574\uc11c $ b$ \ub97c \uc591\ubcc0\uc5d0\uc11c \uc9c0\uc6b0\uace0 $ AB=I$ \ub97c \uc5bb\uc744 \uc218 \uc5c6\uc5b4\uc694. &#8211; \uae40\uc601\uc6b1 <\/p>\n<p> \u2192 &#8221;ABb = b&#8221; \ub97c \ub9cc\uc871\ud558\ub294 AB\uac00 \ubc18\ub4dc\uc2dc I\uc77c \ud544\uc694\ub294 \uc5c6\uc9c0\ub9cc, AB = I \uc774\uc5b4\ub3c4 \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud558\uc796\uc544\uc694?   \uc591\ubcc0\uc5d0\uc11c b\ub97c \uc9c0\uc6b8 \uc21c \uc5c6\uc9c0\ub9cc, \uc9c1\uad00\uc801\uc73c\ub85c AB = I \ub77c\uace0 \uc0dd\uac01\ud560 \uc218 \uc788\uc9c0 \uc54a\ub098\uc694? <\/p>\n<p> A:  \uc6b0\uc120 $ AB$ \ub294 $ I$ \uac00 \ub420 \uc218\uac00 \uc5c6\uc5b4\uc694. \uc815\uc0ac\uac01\ud589\ub82c\uc774 \uc544\ub2cc $ A$ \uc911\uc5d0\uc11c $ AB=I$ \uac00 \ub418\ub294 \uacbd\uc6b0\uac00 \uc65c \uc874\uc7ac\ud560 \uc218 \uc5c6\ub294\uc9c0 \uc0dd\uac01\ud574 \ubcf4\uc138\uc694. (\ubb3c\ub860 $ m&gt;n$ \uc77c \ub54c \uc785\ub2c8\ub2e4.) <\/p>\n<p> \uc9c1\uad00\uc801\uc73c\ub85c \uc0dd\uac01\ud55c\ub2e4\ub294 \uac83\uc774 \ubb34\uc2a8 \ub73b\uc778\uac00\uc694? \ud55c\ubc88 \uc774\ub807\uac8c \ub418\ub294 A, B, b\ub97c \ud558\ub098 \ub9cc\ub4e4\uc5b4\uc11c \uacc4\uc0b0\ud558\uba74\uc11c \uc5b4\ub5bb\uac8c \ub418\ub294\uc9c0 \ud574\ubcf4\uc138\uc694. \uc774 \uad6c\uccb4\uc801\uc778 \uacc4\uc0b0\uc5d0\uc11c $ ABb=b$ \uc774\uc9c0\ub9cc $ AB&not;=I$ \uc778 \uac83\uc744 \ud655\uc778\ud574 \ubcf4\uc138\uc694. <\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\uacf5\uc9c0\uc0ac\ud56d \uc219\uc81c \uc81c\ucd9c\uc740 Exercises section \ud558\ub098\uc529 \uc81c\ucd9c\ud569\ub2c8\ub2e4. &#8221;&#8217;\uc219\uc81c \uc81c\ucd9c \uae30\ud55c\uc740 \uac01 \uc808\uc744 \uc2dc\uc791\ud55c \ub0a0\ub85c\ubd80\ud130 1\uc8fc\uc77c&#8221;&#8217;\uc785\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uba74 1.4\uc808\uc744 \uc6d4\uc694\uc77c\uc5d0 \uc2dc\uc791\ud588\uc73c\uba74 \ub2e4\uc74c \uc8fc \uc6d4\uc694\uc77c &#8221;&#8217;\uac15\uc758\uc2dc\uac04 \uc804\uae4c\uc9c0&#8221;&#8217; 1.4\uc808\uc758 \ubb38\uc81c\ub97c \ud480\uc5b4 \uc81c\ucd9c\ud569\ub2c8\ub2e4. \uc219\uc81c \uc81c\ucd9c\uc740 \uc219\uc81c \uc81c\ucd9c \ubc15\uc2a4\ub97c \uc774\uc6a9\ud569\ub2c8\ub2e4. \uc219\uc81c: 2k11s_LA_exercises.pdf : \uc774 \ud30c\uc77c\uc740 \uacc4\uc18d\ud574\uc11c \uc5c5\ub370\uc774\ud2b8 \ub429\ub2c8\ub2e4. (UploadFile) \uc5f0\uc2b5 2011\ub144 6\uc6d410\uc77c\uae4c\uc9c0 \uc219\uc81c\ud568\uc5d0 \uc219\uc81c \ub123\uc5b4 \ub450\uaca0\uc2b5\ub2c8\ub2e4. \ucc3e\uc544\uac00\uc138\uc694. 2011\ub144 6\uc6d408\uc77c Least &#8230; <a title=\"\uc120\ud615\ub300\uc218 I (2011 \ubd04)\" class=\"read-more\" href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2011\/06\/10\/%ec%84%a0%ed%98%95%eb%8c%80%ec%88%98-i-2011-%eb%b4%84\/\" aria-label=\"\uc120\ud615\ub300\uc218 I (2011 \ubd04)\uc5d0 \ub300\ud574 \ub354 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uc138\uc694\">\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":[11],"tags":[],"class_list":["post-3278","post","type-post","status-publish","format-standard","hentry","category-lectures"],"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\/3278","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=3278"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3278\/revisions"}],"predecessor-version":[{"id":3279,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3278\/revisions\/3279"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3278"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3278"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3278"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}