{"id":5422,"date":"2020-10-15T13:36:33","date_gmt":"2020-10-15T04:36:33","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?p=5422"},"modified":"2020-10-15T15:41:59","modified_gmt":"2020-10-15T06:41:59","slug":"linear-algebra-dual-basis","status":"publish","type":"post","link":"https:\/\/sasamath.com\/blog\/articles\/linear-algebra-dual-basis\/","title":{"rendered":"\uc30d\ub300\uacf5\uac04\uc758 \uae30\uc800"},"content":{"rendered":"

\\(V\\)\uac00 \uccb4 \\(F\\) \uc704\uc5d0\uc11c\uc758 \ubca1\ud130\uacf5\uac04\uc774\ub77c\uace0 \ud558\uc790. \\(F\\)\ub294 \uc790\uae30 \uc790\uc2e0 \uc704\uc5d0\uc11c \uc815\uc758\ub41c \\(1\\)\ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc774\ub2e4. \uc774\ub7ec\ud55c \uad00\uc810\uc5d0\uc11c \\(V\\)\ub85c\ubd80\ud130 \\(F\\)\ub85c\uc758 \ubaa8\ub4e0 \uc120\ud615\ubcc0\ud658\ub4e4\uc758 \ubaa8\uc784\uc744 \\(V^*\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub9cc\uc57d \uc784\uc758\uc758 \\(f,\\,g \\in V^*\\)\uc640 \\(\\lambda \\in F\\)\uc5d0 \ub300\ud558\uc5ec \\(f+g\\)\uc640 \\(\\lambda f\\)\ub97c \ubaa8\ub4e0 \\(x\\in V\\)\uc5d0 \ub300\ud558\uc5ec
\n\\[\\begin{gather} (f+g)(x) = f(x) + g(x), \\\\[6pt]
\n(\\lambda f)(x) = \\lambda (f(x)) \\end{gather}\\]
\n\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \ud568\uc218\ub85c \uc815\uc758\ud558\uba74 \\(V^*\\)\ub294 \ubca1\ud130\uacf5\uac04\uc774 \ub41c\ub2e4. \uc774\ub54c \\(V^*\\)\ub97c \\(V\\)\uc758 \uc30d\ub300\uacf5\uac04<\/span>(dual space)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. [\uc30d\ub300\uacf5\uac04\uc740 \ub300\uc218\uc801 \uc30d\ub300\uacf5\uac04\uacfc \uc5f0\uc18d \uc30d\ub300\uacf5\uac04\uc774 \uc788\ub2e4. \uc774 \uae00\uc5d0\uc11c \ub2e4\ub8e8\ub294 \uc30d\ub300\uacf5\uac04\uc740 \ub300\uc218\uc801 \uc30d\ub300\uacf5\uac04\uc744 \uc774\ub978\ub2e4.]<\/p>\n

\uc774\uc81c \\(V\\)\uc758 \uae30\uc800\uc640 \\(V^*\\)\uc758 \uae30\uc800\uc758 \uad00\uacc4\ub97c \uc0b4\ud3b4\ubcf4\uc790. \\(B = \\left\\{ v_i \\,\\,\\vert\\, i\\in I\\right\\}\\)\ub97c \\(V\\)\uc758 \uae30\uc800\ub77c\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \uac01 \\(i\\in I\\)\uc5d0 \ub300\ud558\uc5ec \ud568\uc218 \\(v_i ^* \\in V^*\\)\ub97c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud558\uc790. \uba3c\uc800 \\(V\\)\uc758 \uae30\uc800\uc6d0\uc18c \\(v_j\\)\uc5d0 \ub300\ud574\uc11c\ub294
\n\\[v_i ^* (v_j ) = \\begin{cases}
\n1 & \\mathrm{if} \\,\\, i=j \\\\[6pt]
\n0 & \\mathrm{if} \\,\\, i\\ne j
\n\\end{cases}\\]
\n\ub85c \uc815\uc758\ud55c\ub2e4. \uadf8\ub9ac\uace0 \\(v_i^*\\)\uc758 \uc120\ud615\uc131\uc774 \uc720\uc9c0\ub418\ub3c4\ub85d \uc815\uc758\uc5ed\uc744 \\(V\\)\ub85c \ud655\uc7a5\ud55c\ub2e4. \\(v_i^*\\)\ub294 \\(V\\)\uc758 \ubaa8\ub4e0 \uae30\uc800\uc6d0\uc18c\uc5d0 \ub300\ud558\uc5ec \uc815\uc758\ub418\uc5b4 \uc788\uc73c\ubbc0\ub85c, \\(V\\) \uc704\uc5d0\uc11c\uc758 \uc120\ud615\ubcc0\ud658\uc73c\ub85c\uc11c \uc720\uc77c\ud558\uac8c \uacb0\uc815\ub41c\ub2e4. \uc774\ub54c \uc9d1\ud569
\n\\[B^* = \\left\\{ v_i ^* \\,\\vert\\, i\\in I\\right\\}\\]
\n\ub97c \\(B\\)\uc758 \uc30d\ub300\uc9d1\ud569<\/span>(dual set)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n

\\(B^*\\)\uac00 \uc77c\ucc28\ub3c5\ub9bd\uc784\uc744 \uc99d\uba85\ud574 \ubcf4\uc790. \\(B^*\\)\uc758 \uc6d0\uc18c \uc911 \uc784\uc758\ub85c \\(n\\)\uac1c\ub97c \ud0dd\ud558\uc790. \uadf8\uac83\uc744
\n\\[v_1^* ,\\,\\, v_2^* ,\\,\\, \\cdots ,\\,\\, v_n ^*\\tag{1}\\]
\n\uc774\ub77c\uace0 \ud558\uc790. \\(\\lambda_i\\)\uac00 \uc2a4\uce7c\ub77c\uc774\uace0
\n\\[\\lambda_1 v_1^* + \\lambda_2 v_2 ^* + \\cdots + \\lambda_n v_n^* = \\mathbf{0}\\tag{2}\\]
\n\uc744 \ub9cc\uc871\uc2dc\ud0a8\ub2e4\uace0 \uac00\uc815\ud558\uc790. \uc774 \ub4f1\uc2dd\uc740 \uc88c\ubcc0\uc758 \ud568\uc218\uc758 \uac12\uc774 \ud56d\ub4f1\uc801\uc73c\ub85c \\(0\\)\uc784\uc744 \uc758\ubbf8\ud558\ubbc0\ub85c, \uc784\uc758\uc758 \\(v\\in V\\)\uc5d0 \ub300\ud558\uc5ec
\n\\[\\lambda_1 v_1^* (v) + \\lambda_2 v_2 ^* (v) + \\cdots + \\lambda_n v_n^* (v)= 0\\tag{3}\\]
\n\uc774 \uc131\ub9bd\ud574\uc57c \ud55c\ub2e4. \ub354\uc6b1\uc774 \uc774 \ub4f1\uc2dd\uc740 \\(v=v_i,\\) \\(i = 1,\\,2,\\,\\cdots,\\,n\\)\uc77c \ub54c\uc5d0\ub3c4 \uc131\ub9bd\ud574\uc57c \ud55c\ub2e4. \\(v=v_i\\)\ub97c \ub300\uc785\ud558\uba74 (3)\uc73c\ub85c\ubd80\ud130 \ub2e4\uc74c\uc744 \uc5bb\ub294\ub2e4.
\n\\[\\lambda_i ^* =0\\]
\n\uc5ec\uae30\uc11c \\(i\\)\ub294 \\(n\\) \uc774\ud558\uc778 \uc784\uc758\uc758 \uc790\uc5f0\uc218\uc774\ubbc0\ub85c (1)\uc740 \uc77c\ucc28\ub3c5\ub9bd\uc774\ub2e4. (1)\uc740 \\(B^*\\)\uc758 \uc6d0\uc18c \uc911 \uc720\ud55c \uac1c\ub97c \uc784\uc758\ub85c \ud0dd\ud55c \uac83\uc774\ubbc0\ub85c \\(B^*\\)\ub294 \uc77c\ucc28\ub3c5\ub9bd\uc774\ub2e4.<\/p>\n

\ub9cc\uc57d \\(B^*\\)\uac00 \\(V^*\\)\ub97c \uc0dd\uc131\ud558\uba74 \\(B^*\\)\ub294 \\(V^*\\)\uc758 \uae30\uc800\uac00 \ub420 \uac83\uc774\ub2e4. \uc774\uac83\uc740 \\(V\\)\uc758 \ucc28\uc6d0\uc5d0 \ub530\ub77c \ub2e4\ub974\ub2e4.<\/p>\n

\n

\uc815\ub9ac 1.<\/span>
\n\\(V\\)\uac00 \uc720\ud55c\ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc774\uace0 \\(B\\)\uac00 \\(V\\)\uc758 \uae30\uc800\uc774\uba74 \\(B\\)\uc758 \uc30d\ub300\uc9d1\ud569 \\(B^*\\)\ub294 \uc30d\ub300\uacf5\uac04 \\(V^*\\)\uc758 \uae30\uc800\uc774\ub2e4.\n<\/p>\n<\/div>\n

\n

\uc99d\uba85<\/p>\n

\uc55e\uc5d0\uc11c \uc774\ubbf8 \\(B^*\\)\uac00 \uc77c\ucc28\ub3c5\ub9bd\uc784\uc744 \ubcf4\uc600\uc73c\ubbc0\ub85c, \\(B^*\\)\uac00 \\(V^*\\)\ub97c \uc0dd\uc131\ud55c\ub2e4\ub294 \uc0ac\uc2e4\ub9cc \ubcf4\uc774\uba74 \ub41c\ub2e4.<\/p>\n

\\(V\\)\uc758 \ucc28\uc6d0\uc744 \\(n\\)\uc774\ub77c\uace0 \ud558\uace0
\n\\[B = \\left\\{ v_1 ,\\, v_2 ,\\ \\cdots ,\\, v_n \\right\\}\\]
\n\ub85c \ub098\ud0c0\ub0b4\uc790. \uc774\uc81c \\(f^* \\in V^*\\)\uac00 \uc784\uc758\ub85c \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \uac01 \\(i\\)\uc5d0 \ub300\ud558\uc5ec
\n\\[\\lambda_i ^* = f^* (v_i )\\]
\n\ub77c\uace0 \uc815\uc758\ud558\uc790. \uadf8\ub7ec\uba74 \uc784\uc758\uc758 \\(v\\in V\\)\uc5d0 \ub300\ud558\uc5ec
\n\\[v = \\lambda_1 v_1 + \\lambda_2 v_2 + \\cdots + \\lambda_n v_n\\]
\n\uc778 \uc2a4\uce7c\ub77c \\(\\lambda_i\\)\uac00 \uc874\uc7ac\ud558\uba70, \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.
\n\\[\\begin{align}
\nf^*(v)
\n&= f^* ( \\lambda_1 v_1 + \\lambda_2 v_2 + \\cdots + \\lambda_n v_n ) \\\\[7pt]
\n&= \\lambda_1 f^* (v_1) + \\lambda_2 f^* (v_2) + \\cdots + \\lambda_n f^* (v_n) \\\\[7pt]
\n&= \\lambda_1 \\lambda_1^* + \\lambda_2 \\lambda_2^* + \\cdots + \\lambda_n \\lambda_n^* \\\\[7pt]
\n&= \\lambda_1^* \\lambda_1 v_1^* (v_1) + \\lambda_2^* \\lambda_2 v_2^* (v_2) + \\cdots + \\lambda_n^* \\lambda_n v_n^* (v_n) \\\\[7pt]
\n&= \\lambda_1^* v_1^* (\\lambda_1 v_1 ) + \\lambda_2^* v_2^* (\\lambda_2 v_2 ) +\\cdots + \\lambda_n^* v_n^* (\\lambda_n v_n ) \\\\[7pt]
\n&= \\lambda_1^* v_1^* (v) + \\lambda_2^* v_2^* (v) + \\cdots + \\lambda_n^* v_n^* (v).
\n\\end{align}\\]
\n\uc989 \\(f^*\\)\ub294 \\(v_1^* ,\\) \\(v_2 ^*,\\) \\(\\cdots,\\) \\(v_n^*\\)\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ud45c\ud604\ub41c\ub2e4.<\/p>\n

\\(f^*\\)\ub294 \\(V^*\\)\uc5d0\uc11c \uc784\uc758\ub85c \ud0dd\ud55c \uc6d0\uc18c\uc774\ubbc0\ub85c \\(B^*\\)\ub294 \\(V^*\\)\ub97c \uc0dd\uc131\ud55c\ub2e4.
\n<\/span><\/p>\n<\/div>\n

\uc704 \uc815\ub9ac\uc5d0\uc11c \\(B^*\\)\uc758 \uc6d0\uc18c\uc758 \uac1c\uc218\uac00 \\(B\\)\uc758 \uc6d0\uc18c\uc758 \uac1c\uc218\uc640 \uac19\uc73c\ubbc0\ub85c \ub2e4\uc74c\uc744 \uc5bb\ub294\ub2e4.<\/p>\n

\n

\ub530\ub984\uc815\ub9ac 2.<\/span>
\n\\(V\\)\uac00 \uc720\ud55c\ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc774\uba74 \\(V^*\\)\uc758 \ucc28\uc6d0\uc740 \\(V\\)\uc758 \ucc28\uc6d0\uacfc \uac19\ub2e4.\n<\/p>\n<\/div>\n

\ud55c\ud3b8 \\(V\\)\uc758 \ucc28\uc6d0\uc774 \ubb34\ud55c\uc77c \ub54c\ub294 \\(B^*\\)\ub294 \\(V^*\\)\uc758 \uae30\uc800\uac00 \ub418\uc9c0 \ubabb\ud55c\ub2e4.<\/p>\n

\n

\uc815\ub9ac 3.<\/span>
\n\\(V\\)\uac00 \ubb34\ud55c\ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc774\uace0 \\(B\\)\uac00 \\(V\\)\uc758 \uae30\uc800\ub77c\uace0 \ud558\uc790. \uc774\ub54c \\(B\\)\uc758 \uc30d\ub300\uc9d1\ud569 \\(B^*\\)\ub294 \uc30d\ub300\uacf5\uac04 \\(V^*\\)\ub97c \uc0dd\uc131\ud558\uc9c0 \ubabb\ud55c\ub2e4.\n<\/p>\n<\/div>\n

\n

\uc99d\uba85<\/p>\n

\\(V\\)\uc758 \ucc28\uc6d0\uc774 \ubb34\ud55c\uc774\ubbc0\ub85c \\(B = \\left\\{ v_i \\,\\vert\\, i\\in I\\right\\}\\)\uac00 \ubb34\ud55c\uc9d1\ud569\uc774\ub2e4. \uc989 \\(I\\)\uac00 \ubb34\ud55c\uc9d1\ud569\uc774\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \\(I\\)\ub97c \uc11c\ub85c\uc18c\uc778 \ub450 \ubb34\ud55c\uc9d1\ud569 \\(J,\\) \\(K\\)\uc758 \ud569 \\(I = J\\cup K\\)\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \ud568\uc218 \\(g^*\\in V^*\\)\ub97c \\(B\\)\uc758 \uc6d0\uc18c \\(v_j\\)\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud558\uc790.
\n\\[g^*(v_j) =
\n\\begin{cases}
\n1 & \\text{if} \\,\\, j\\in J \\\\[7pt]
\n0 & \\text{if} \\,\\, j\\in K
\n\\end{cases}\\]
\n\uadf8\ub9ac\uace0 \\(g^*\\)\uc758 \uc120\ud615\uc131\uc774 \uc720\uc9c0\ub418\ub3c4\ub85d \uc815\uc758\uc5ed\uc744 \\(V\\)\ub85c \ud655\uc7a5\ud558\uc790. \uadf8\ub7ec\uba74 \\(g^*\\)\ub294 \uc720\ud55c \uac1c\uc758 \\(v_i ^*\\)\ub4e4\uc758 \uc77c\ucc28\uacb0\ud569\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc5c6\ub2e4. \uc989 \\(g^*\\)\ub294 \\(B^*\\)\uc5d0 \uc758\ud558\uc5ec \uc0dd\uc131\ub418\ub294 \ubca1\ud130\uacf5\uac04\uc5d0 \uc18d\ud558\uc9c0 \uc54a\ub294\ub2e4.
\n<\/span><\/p>\n<\/div>\n

\\(V\\)\uc758 \uae30\uc800 \\(B\\)\uc758 \uc30d\ub300\uc9d1\ud569 \\(B^*\\)\uac00 \uc30d\ub300\uacf5\uac04 \\(V^*\\)\uc758 \uae30\uc800\uac00 \ub420 \ub54c \\(B^*\\)\ub97c \\(V^*\\)\uc758 \uc30d\ub300\uae30\uc800<\/span>(dual basis)\ub77c\uace0 \ubd80\ub978\ub2e4. \uc9c0\uae08\uae4c\uc9c0 \uc0b4\ud3b4\ubcf8 \ub0b4\uc6a9\uc744 \uc694\uc57d\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n

\n

\\(V\\)\uac00 \ubca1\ud130\uacf5\uac04\uc774\uace0 \\(B\\)\uac00 \\(V\\)\uc758 \uae30\uc800\ub77c\uace0 \ud558\uc790. \\(B^*\\)\uac00 \\(V^*\\)\uc758 \uc30d\ub300\uae30\uc800\uac00 \ub420 \ud544\uc694\ucda9\ubd84\uc870\uac74\uc740 \\(V\\)\uc758 \ucc28\uc6d0\uc774 \uc720\ud55c\uc778 \uac83\uc774\ub2e4. \ub354\uc6b1\uc774 \\(V\\)\uac00 \uc720\ud55c\ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc774\uba74 \\(V\\)\uc758 \ucc28\uc6d0\uacfc \\(V^*\\)\uc758 \ucc28\uc6d0\uc774 \uac19\ub2e4.<\/p>\n<\/div>\n

\uc774\uc81c \ub2e4\uc74c \ubb3c\uc74c\uc5d0 \ub2f5\ud574\ubcf4\uae30 \ubc14\ub780\ub2e4.<\/p>\n

    \n
  • \\(V\\)\uac00 \ubca1\ud130\uacf5\uac04\uc77c \ub54c \\(V\\)\uc758 \uc30d\ub300\uacf5\uac04\uc758 \uc30d\ub300\uacf5\uac04\uc744 \\(V\\)\uc758 \uc774\uc911\uc30d\ub300\uacf5\uac04<\/span>\uc774\ub77c\uace0 \ubd80\ub974\uace0 \\(V^{**}\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. (\u2018second dual space\u2019 \ub610\ub294 \u2018double dual space\u2019.) \\(V\\)\uac00 \uc720\ud55c\ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc77c \ub54c \\(V^{**}\\)\uc758 \uae30\uc800\uc758 \ubaa8\uc591\uc744 \uae30\uc220\ud558\uace0, \\(V\\)\uc640 \\(V^{**}\\)\uac00 \ub3d9\ud615\uc784\uc744 \uc99d\uba85\ud574 \ubcf4\uc790.<\/li>\n
  • \uc704\uc0c1\ubca1\ud130\uacf5\uac04<\/span>(topological vector space)\uc758 \uc815\uc758\ub97c \uc870\uc0ac\ud574 \ubcf4\uc790. \uadf8\ub9ac\uace0 \\(V\\)\uac00 \uc704\uc0c1\ubca1\ud130\uacf5\uac04\uc77c \ub54c \\(V\\)\uc640 \\(V^{*}\\)\uc758 \uad00\uacc4, \uadf8\ub9ac\uace0 \\(V\\)\uc640 \\(V^{**}\\)\uc758 \uad00\uacc4\ub97c \uc870\uc0ac\ud574 \ubcf4\uc790.<\/li>\n<\/ul>\n

    <\/p>\n","protected":false},"excerpt":{"rendered":"

    \\(V\\)\uac00 \uccb4 \\(F\\) \uc704\uc5d0\uc11c\uc758 \ubca1\ud130\uacf5\uac04\uc774\ub77c\uace0 \ud558\uc790. \\(F\\)\ub294 \uc790\uae30 \uc790\uc2e0 \uc704\uc5d0\uc11c \uc815\uc758\ub41c \\(1\\)\ucc28\uc6d0 \ubca1\ud130\uacf5\uac04\uc774\ub2e4. \uc774\ub7ec\ud55c \uad00\uc810\uc5d0\uc11c \\(V\\)\ub85c\ubd80\ud130 \\(F\\)\ub85c\uc758 \ubaa8\ub4e0 \uc120\ud615\ubcc0\ud658\ub4e4\uc758 \ubaa8\uc784\uc744 \\(V^*\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub9cc\uc57d \uc784\uc758\uc758 \\(f,\\,g \\in V^*\\)\uc640 \\(\\lambda \\in F\\)\uc5d0 \ub300\ud558\uc5ec \\(f+g\\)\uc640 \\(\\lambda f\\)\ub97c \ubaa8\ub4e0 \\(x\\in V\\)\uc5d0 \ub300\ud558\uc5ec \\(\\begin{gather} (f+g)(x) = f(x) + g(x), (\\lambda f)(x) = \\lambda (f(x)) \\end{gather}\\) \ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \ud568\uc218\ub85c \uc815\uc758\ud558\uba74 \\(V^*\\)\ub294 \ubca1\ud130\uacf5\uac04\uc774 \ub41c\ub2e4. \uc774\ub54c \\(V^*\\)\ub97c \\(V\\)\uc758 \uc30d\ub300\uacf5\uac04(dual space)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[57],"tags":[437,436,434,435],"class_list":["post-5422","post","type-post","status-publish","format-standard","hentry","category-linear-algebra","tag-dual-basis","tag-dual-space","tag-434","tag-435"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/5422","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=5422"}],"version-history":[{"count":28,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/5422\/revisions"}],"predecessor-version":[{"id":5450,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/5422\/revisions\/5450"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=5422"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/categories?post=5422"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/tags?post=5422"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}