{"id":387,"date":"2021-04-25T13:22:03","date_gmt":"2021-04-25T05:22:03","guid":{"rendered":"http:\/\/www.wayln.com\/?p=387"},"modified":"2021-04-29T20:50:21","modified_gmt":"2021-04-29T12:50:21","slug":"4-2-%e9%9b%b6%e7%a9%ba%e9%97%b4%e3%80%81%e5%88%97%e7%a9%ba%e9%97%b4%e5%92%8c%e7%ba%bf%e6%80%a7%e5%8f%98%e6%8d%a2","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=387","title":{"rendered":"4.2 \u96f6\u7a7a\u95f4\u3001\u5217\u7a7a\u95f4\u548c\u7ebf\u6027\u53d8\u6362"},"content":{"rendered":"<div id=\"toc_container\" class=\"toc_transparent no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u77e9\u9635\u7684\u96f6\u7a7a\u95f4<\/a><\/li><li><a href=\"#NulA\"><span class=\"toc_number toc_depth_1\">2<\/span> NulA\u7684\u4e00\u4e2a\u663e\u5f0f\u523b\u753b<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">3<\/span> \u77e9\u9635\u7684\u5217\u7a7a\u95f4<\/a><\/li><li><a href=\"#NulAColA\"><span class=\"toc_number toc_depth_1\">4<\/span> NulA\u4e0eColA\u4e4b\u95f4\u7684\u5bf9\u6bd4<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">5<\/span> \u7ebf\u6027\u53d8\u6362\u7684\u6838\u4e0e\u503c\u57df<\/a><\/li><\/ul><\/div>\n<p>\u5728\u7ebf\u6027\u4ee3\u6570\u7684\u5e94\u7528\u4e2d\uff0c<span class=\"katex math inline\">R^n<\/span>\u7684\u5b50\u7a7a\u95f4\u901a\u5e38\u7531\u4ee5\u4e0b\u4e24\u79cd\u65b9\u5f0f\u4ea7\u751f\uff1a(1)\u9f50\u6b21\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u89e3\u96c6\u6216\uff082\uff09\u67d0\u4e9b\u786e\u5b9a\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u7684\u96c6\u5408\u3002<\/p>\n<h1><span id=\"i\">\u77e9\u9635\u7684\u96f6\u7a7a\u95f4<\/span><\/h1>\n<p>\u8003\u8651\u4e0b\u5217\u9f50\u6b21\u65b9\u7a0b\u7ec4<\/p>\n<div class=\"katex math multi-line no-emojify\">\\begin{cases}<br \/>\nx_1-3x_2-2x_3=0\\\\<br \/>\n-5x_1+9x_2+x_3=0 \\tag{1}<br \/>\n\\end{cases}\n<\/div>\n<p>\u7528\u77e9\u9635\u7684\u65b9\u5f0f\uff0c\u6b21\u65b9\u7a0b\u7ec4\u53ef\u5199\u6210Ax=0,\u8fd9\u91cc<\/p>\n<div class=\"katex math multi-line no-emojify\">A=\\left[\\begin{array}{rrr}<br \/>\n1&amp;-3&amp;-2\\\\<br \/>\n-5&amp;9&amp;1 \\tag{2}<br \/>\n\\end{array}\\right]\n<\/div>\n<p>\u6240\u6709\u6ee1\u8db3\uff081\uff09\u7684x\u7684\u96c6\u5408\u6210\u4e3a\u65b9\u7a0b\u7ec4(1)\u7684<strong>\u89e3\u96c6<\/strong>\uff0c\u901a\u5e38\u5c06\u8fd9\u4e2a\u89e3\u96c6\u76f4\u63a5\u4e0e\u77e9\u9635<span class=\"katex math inline\">A<\/span>\u548c\u65b9\u7a0b<span class=\"katex math inline\">Ax=0<\/span>\u8054\u7cfb\u8d77\u6765\u662f\u65b9\u4fbf\u7684\uff0c\u6211\u4eec\u79f0\u6ee1\u8db3<span class=\"katex math inline\">Ax=0<\/span>\u7684\u6240\u6709x\u7684\u96c6\u5408\u4e3a\u77e9\u9635A\u7684\u96f6\u7a7a\u95f4\u3002<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u4e49<\/strong>\u3000mxn\u77e9\u9635A\u7684\u96f6\u7a7a\u95f4\u5199\u6210<span class=\"katex math inline\">NulA<\/span>,\u662f\u9f50\u6b21\u65b9\u7a0b<span class=\"katex math inline\">Ax=0<\/span>\u7684\u5168\u4f53\u89e3\u7684\u96c6\u5408\uff0c\u7528\u96c6\u5408\u7b26\u53f7\u8868\u793a\u5373<\/p>\n<div class=\"katex math multi-line no-emojify\">NulA=\\{x:x\\in R^n,Ax=0 \\}\n  <\/div>\n<\/blockquote>\n<p><span class=\"katex math inline\">NulA<\/span>\u7684\u66f4\u8fdb\u4e00\u6b65\u7684\u63cf\u8ff0\u4e3a<span class=\"katex math inline\">R^n<\/span>\u4e2d\u5728\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">x \\mapsto Ax<\/span>\u4e0b\u6620\u5c04\u5230<span class=\"katex math inline\">R^n<\/span>\u4e2d\u96f6\u5411\u91cf\u7684\u5eaa\u5411\u91cf\u7684\u96c6\u5408\uff0c\u89c1\u4e0b\u56fe<br \/>\n<a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_31403875959facaf152d54294937eae1.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_31403875959facaf152d54294937eae1.jpg\" alt=\"\" \/><\/a><\/p>\n<blockquote><p>\n  <strong>\u5b9a\u74062<\/strong>\u3000mxn\u77e9\u9635A\u7684\u96f6\u7a7a\u95f4\u662f<span class=\"katex math inline\">R^n<\/span>\u7684\u4e00\u4e2a\u5b50\u7a7a\u95f4\uff0c\u7b49\u4ef7\u7684\uff0cm\u4e2a\u65b9\u7a0b\u3001n\u4e2a\u672a\u77e5\u6570\u7684\u9f50\u6b21\u65b9\u7a0b\u7ec4<span class=\"katex math inline\">Ax=0<\/span>\u7684\u5168\u4f53\u89e3\u7684\u96c6\u5408\u662f<span class=\"katex math inline\">R^n<\/span>\u7684\u4e00\u4e2a\u5b50\u7a7a\u95f4\u3002\n<\/p><\/blockquote>\n<h1><span id=\"NulA\">NulA\u7684\u4e00\u4e2a\u663e\u5f0f\u523b\u753b<\/span><\/h1>\n<p>NulA\u4e2d\u7684\u5411\u91cf\u4e0eA\u4e2d\u7684\u6570\u503c\u4e4b\u95f4\u6ca1\u6709\u660e\u663e\u7684\u5173\u7cfb\u3002\u6211\u4eec\u79f0NulA\u88ab\u9690\u5f0f\u5730\u5b9a\u4e49\uff0c\u8fd9\u662f\u7531\u4e8e\u5b83\u88ab\u4e00\u4e2a\u5fc5\u987b\u8981\u68c0\u9a8c\u7684\u6761\u4ef6\u6240\u5b9a\u4e49\uff0c\u6ca1\u6709\u660e\u786e\u5730\u7ed9\u51faNulA\u4e2d\u5143\u7d20\u3002\u7136\u800c\uff0c\u5f53\u6211\u4eec\u89e3\u51fa\u65b9\u7a0bAx=0\uff0c\u6211\u4eec\u5c31\u5f97\u5230NulA\u7684\u663e\u5f0f\u523b\u753b\u3002<\/p>\n<h1><span id=\"i-2\">\u77e9\u9635\u7684\u5217\u7a7a\u95f4<\/span><\/h1>\n<p>\u4e0e\u77e9\u9635\u76f8\u5173\u7684\u53e6\u4e00\u4e2a\u91cd\u8981\u7684\u5b50\u7a7a\u95f4\u662f\u5b83\u7684\u5217\u7a7a\u95f4\u3002\u4e0e\u96f6\u7a7a\u95f4\u4e0d\u540c\uff0c\u5217\u7a7a\u95f4\u53ef\u4ee5\u7531\u5411\u91cf\u7684\u7ebf\u6027\u7ec4\u5408\u663e\u5f0f\u5b9a\u4e49<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u4e49<\/strong>\u3000mxn\u77e9\u9635\u7684\u5217\u7a7a\u95f4\uff08\u8bb0\u4e3aColA\uff09\u662f\u7531A\u7684\u5217\u7684\u6240\u6709\u7ebf\u6027\u7ec4\u5408\u7ec4\u6210\u7684\u96c6\u5408\uff0c\u82e5<span class=\"katex math inline\">A=\\begin{bmatrix}a_1,\\dots,a_n \\end{bmatrix}<\/span>,\u5219<span class=\"katex math inline\">ColA=Span&#92;{a_1,\\dots,a_n&#92;}<\/span>\u3002<\/p>\n<p>  <strong>\u5b9a\u74063<\/strong> mxn\u77e9\u9635A\u7684\u5217\u7a7a\u95f4\u65f6<span class=\"katex math inline\">R^m<\/span>\u7684\u4e00\u4e2a\u5b50\u7a7a\u95f4\n<\/p><\/blockquote>\n<p>\u6ce8\u610f\u5230ColA\u4e2d\u4e00\u4e2a\u5178\u578b\u5411\u91cf\u53ef\u5199\u6210<span class=\"katex math inline\">Ax<\/span>\u7684\u5f62\u52bf\uff0c\u5176\u4e2dx\u4e3a\u67d0\u5411\u91cf\uff0c\u56e0\u4e3a\u8bb0\u53f7<span class=\"katex math inline\">Ax<\/span>\u8868\u793aA\u7684\u5217\u5411\u91cf\u7684\u4e00\u4e2a\u7ebf\u6027\u7ec4\u5408\uff0c\u5373<\/p>\n<div class=\"katex math multi-line no-emojify\">ColA=\\{b:b=Ax,x \\in R^n\\}\n<\/div>\n<p>\u4ee3\u8868ColA\u4e2d\u5411\u91cf\u7684\u8bb0\u53f7<span class=\"katex math inline\">Ax<\/span>\u4e5f\u8868\u660e<span class=\"katex math inline\">ColA<\/span>\u662f\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">x \\mapsto Ax<\/span>\u7684\u503c\u57df\u3002<\/p>\n<blockquote><p>\n  mxn\u77e9\u9635A\u7684\u5217\u7a7a\u95f4\u7b49\u4e8e<span class=\"katex math inline\">R^m<\/span>\u5f53\u4e14\u4ec5\u5f53\u65b9\u7a0b<span class=\"katex math inline\">Ax=b<\/span>\u5bf9<span class=\"katex math inline\">R^m<\/span>\u4e2d\u6bcf\u4e2ab\u6709\u4e00\u4e2a\u89e3\n<\/p><\/blockquote>\n<h1><span id=\"NulAColA\">NulA\u4e0eColA\u4e4b\u95f4\u7684\u5bf9\u6bd4<\/span><\/h1>\n<p>\u4e00\u4e2a\u77e9\u9635\u7684\u96f6\u7a7a\u95f4\u548c\u5217\u7a7a\u95f4\u4e4b\u95f4\u7684\u5173\u7cfb\u5982\u4f55\u662f\u4e00\u4e2a\u81ea\u7136\u7684\u95ee\u9898\uff0c\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u4e24\u4e2a\u7a7a\u95f4\u662f\u5f88\u4e0d\u4e00\u6837\u7684\u3002<\/p>\n<table>\n<thead>\n<tr>\n<th>NulA<\/th>\n<th>ColA<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1. <span class=\"katex math inline\">NulA<\/span>\u662f<span class=\"katex math inline\">R^n<\/span>\u7684\u4e00\u4e2a\u5b50\u7a7a\u95f4<\/td>\n<td>1. <span class=\"katex math inline\">ColA<\/span>\u662f<span class=\"katex math inline\">R^m<\/span>\u7684\u4e00\u4e2a\u5b50\u7a7a\u95f4<\/td>\n<\/tr>\n<tr>\n<td>2. <span class=\"katex math inline\">NulA<\/span>\u662f\u9690\u5f0f\u5b9a\u4e49\u7684\uff0c\u5373\u4ec5\u7ed9\u51fa\u4e00\u4e2a<span class=\"katex math inline\">NulA<\/span>\u4e2d\u5411\u91cf\u5fc5\u987b\u6ee1\u8db3\u7684\u6761\u4ef6(<span class=\"katex math inline\">Ax=0<\/span>)<\/td>\n<td>2. <span class=\"katex math inline\">ColA<\/span>\u662f\u663e\u5f0f\u5b9a\u4e49\uff0c\u5373\u660e\u786e\u6307\u51fa\u5982\u4f55\u5efa\u7acb<span class=\"katex math inline\">ColA<\/span>\u4e2d\u7684\u5411\u91cf<\/td>\n<\/tr>\n<tr>\n<td>3. \u6c42<span class=\"katex math inline\">NulA<\/span>\u4e2d\u7684\u5411\u91cf\u9700\u8981\u65f6\u95f4\uff0c\u9700\u8981\u5bf9<span class=\"katex math inline\">\\begin{bmatrix}A&amp;0\\end{bmatrix}<\/span>\u505a\u884c\u53d8\u6362<\/td>\n<td>3. \u5bb9\u6613\u6c42\u51fa<span class=\"katex math inline\">ColA<\/span>\u4e2d\u7684\u5411\u91cf\uff0c<span class=\"katex math inline\">A<\/span>\u4e2d\u7684\u5217\u5c31\u662f<span class=\"katex math inline\">ColA<\/span>\u4e2d\u7684\u5411\u91cf\uff0c\u5176\u4f59\u7684\u53ef\u7531<span class=\"katex math inline\">A<\/span>\u7684\u5217\u8868\u793a\u51fa\u6765<\/td>\n<\/tr>\n<tr>\n<td>4. <span class=\"katex math inline\">NulA<\/span>\u4e0e<span class=\"katex math inline\">A<\/span>\u7684\u6570\u503c\u4e4b\u95f4\u6ca1\u6709\u660e\u663e\u7684\u5173\u7cfb<\/td>\n<td>4. <span class=\"katex math inline\">ColA<\/span>\u4e0e<span class=\"katex math inline\">A<\/span>\u7684\u6570\u503c\u4e4b\u95f4\u6709\u660e\u663e\u7684\u5173\u7cfb\uff0c\u56e0\u4e3aA\u7684\u5217\u5c31\u5728<span class=\"katex math inline\">ColA<\/span>\u4e2d<\/td>\n<\/tr>\n<tr>\n<td>5. <span class=\"katex math inline\">NulA<\/span>\u4e2d\u7684\u4e00\u4e2a\u5178\u578b\u5411\u91cf<span class=\"katex math inline\">v<\/span>\u5177\u6709<span class=\"katex math inline\">Av=0<\/span>\u7684\u6027\u8d28<\/td>\n<td>5. <span class=\"katex math inline\">ColA<\/span>\u4e2d\u4e00\u4e2a\u5178\u578b\u5411\u91cf<span class=\"katex math inline\">v<\/span>\u5177\u6709\u65b9\u7a0b<span class=\"katex math inline\">Ax=v<\/span>\u662f\u76f8\u5bb9\u7684\u6027\u8d28<\/td>\n<\/tr>\n<tr>\n<td>6. \u7ed9\u4e00\u4e2a\u7279\u5b9a\u7684\u5411\u91cf<span class=\"katex math inline\">v<\/span>,\u5bb9\u6613\u5224\u65ad<span class=\"katex math inline\">v<\/span>\u662f\u5426\u5728<span class=\"katex math inline\">NulA<\/span>\u4e2d\uff0c\u4ec5\u9700\u8ba1\u7b97<span class=\"katex math inline\">Av<\/span><\/td>\n<td>6. \u7ed9\u4e00\u4e2a\u7279\u5b9a\u7684\u5411\u91cf<span class=\"katex math inline\">v<\/span>,\u5f04\u6e05<span class=\"katex math inline\">v<\/span>\u662f\u5426\u5728<span class=\"katex math inline\">ColA<\/span>\u4e2d\u9700\u8981\u65f6\u95f4\uff0c\u9700\u8981\u5bf9<span class=\"katex math inline\">\\begin{bmatrix}A&amp;v\\end{bmatrix}<\/span>\u4f5c\u884c\u53d8\u6362<\/td>\n<\/tr>\n<tr>\n<td>7. <span class=\"katex math inline\">NulA=&#92;{0&#92;}<\/span>\u5f53\u4e14\u4ec5\u5f53\u65b9\u7a0bAx=0\u4ec5\u6709\u4e00\u4e2a\u5e73\u51e1\u89e3<\/td>\n<td>7. <span class=\"katex math inline\">ColA=R^m<\/span>\u5f53\u4e14\u4ec5\u5f53\u65b9\u7a0b<span class=\"katex math inline\">Ax=b<\/span>\u5bf9\u6bcf\u4e00\u4e2a<span class=\"katex math inline\">b \\in R^m<\/span>\u6709\u4e00\u4e2a\u89e3<\/td>\n<\/tr>\n<tr>\n<td>8. <span class=\"katex math inline\">NulA=&#92;{0&#92;}<\/span>\u5f53\u4e14\u4ec5\u5f53\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">x \\mapsto Ax<\/span>\u662f\u4e00\u5bf9\u4e00\u7684<\/td>\n<td>8. <span class=\"katex math inline\">ColA=R^m<\/span>\u5f53\u4e14\u4ec5\u5f53\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">x \\mapsto Ax<\/span>\u5c06<span class=\"katex math inline\">R^n<\/span>\u6620\u4e0a\u5230<span class=\"katex math inline\">R^m<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1><span id=\"i-3\">\u7ebf\u6027\u53d8\u6362\u7684\u6838\u4e0e\u503c\u57df<\/span><\/h1>\n<p>\u6211\u4eec\u7ecf\u5e38\u9700\u8981\u7528\u7ebf\u6027\u53d8\u6362\u800c\u4e0d\u662f\u77e9\u9635\u6765\u8868\u8ff0\u9664<span class=\"katex math inline\">R^n<\/span>\u4ee5\u5916\u7684\u5411\u91cf\u7a7a\u95f4\u7684\u5b50\u7a7a\u95f4<\/p>\n<blockquote><p>\n  <strong>\u5b9a\u4e49<\/strong> \u7531\u5411\u91cf\u7a7a\u95f4V\u6620\u5c04\u5230\u5411\u91cf\u7a7a\u95f4W\u5185\u7684<strong>\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">T<\/span><\/strong>\u662f\u4e00\u4e2a\u89c4\u5219,\u5b83\u5c06<span class=\"katex math inline\">V<\/span>\u4e2d\u6ca1\u4e2a\u5411\u91cf<span class=\"katex math inline\">x<\/span>\u6620\u5c04\u6210<span class=\"katex math inline\">W<\/span>\u4e2d\u552f\u4e00\u5411\u91cf<span class=\"katex math inline\">T(x)<\/span>\uff0c\u4e14\u6ee1\u8db3\uff1a<br \/>\n  (1)\u3000<span class=\"katex math inline\">T(u+v)=T(u)+T(v)<\/span>\uff0c\u5bf9<span class=\"katex math inline\">V<\/span>\u4e2d\u6240\u6709<span class=\"katex math inline\">u,v<\/span>\u5747\u6210\u7acb<br \/>\n  (2)\u3000<span class=\"katex math inline\">T(cu)=cT(u)<\/span>,\u5bf9<span class=\"katex math inline\">V<\/span>\u4e2d\u6240\u6709<span class=\"katex math inline\">u<\/span>\u53ca\u6240\u6709\u6570<span class=\"katex math inline\">c<\/span>\u5747\u6210\u7acb\n<\/p><\/blockquote>\n<p>\u7ebf\u6027\u53d8\u6362<span class=\"katex math inline\">T<\/span>\u7684<strong>\u6838(\u6216\u96f6\u7a7a\u95f4)<\/strong>\u662f<span class=\"katex math inline\">V<\/span>\u4e2d\u6240\u6709\u6ee1\u8db3<span class=\"katex math inline\">T(u)=0<\/span>\u7684\u5411\u91cf<span class=\"katex math inline\">u<\/span>\u7684\u96c6\u5408\uff080\u4e3aW\u4e2d\u7684\u96f6\u5411\u91cf\uff09\uff0c<span class=\"katex math inline\">T<\/span>\u7684<strong>\u503c\u57df<\/strong>\u662f<span class=\"katex math inline\">W<\/span>\u4e2d\u6240\u6709\u5177\u6709\u5f62\u5f0f<span class=\"katex math inline\">T(x)<\/span>\uff08\u4efb\u610f<span class=\"katex math inline\">x \\in V<\/span>\uff09\u7684\u5411\u91cf\u7684\u96c6\u5408\u3002\u5982\u679cT\u662f\u7531\u4e00\u4e2a\u77e9\u9635\u53d8\u6362\u5f97\u5230\u7684\uff0c\u6bd4\u5982\u67d0\u77e9\u9635<span class=\"katex math inline\">A<\/span>\uff0c<span class=\"katex math inline\">T(x)=Ax<\/span>,\u5219<span class=\"katex math inline\">T<\/span>\u7684\u6838\u4e0e\u503c\u57df\u6070\u597d\u662f\u524d\u9762\u5b9a\u4e49\u7684<span class=\"katex math inline\">A<\/span>\u7684\u96f6\u7a7a\u95f4\u548c\u5217\u7a7a\u95f4<br \/>\n<a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_dd48cc4df7e0ea03cd1a94486db7d10e.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_dd48cc4df7e0ea03cd1a94486db7d10e.jpg\" alt=\"\" \/><\/a><\/p>\n<p>\u5728\u5e94\u7528\u4e2d\uff0c\u4e00\u4e2a\u5b50\u7a7a\u95f4\u5f80\u5f80\u7531\u4e00\u4e2a\u9002\u5f53\u7684\u7ebf\u6027\u53d8\u6362\u7684\u6838\u6216\u503c\u57df\u4ea7\u751f\uff0c\u6bd4\u5982\uff0c\u4e00\u4e2a\u9f50\u6b21\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\u7684\u5168\u90e8\u89e3\u7684\u96c6\u5408\u88ab\u5224\u660e\u662f\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u6838\u3002\u5178\u578b\u7684\uff0c\u8fd9\u6837\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u7528\u5173\u4e8e\u4e00\u4e2a\u51fd\u6570\u7684\u4e00\u9636\u6216\u9ad8\u9636\u5bfc\u6570\u63cf\u8ff0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u77e9\u9635\u7684\u96f6\u7a7a\u95f42 NulA\u7684\u4e00\u4e2a\u663e\u5f0f\u523b\u753b3 \u77e9\u9635\u7684\u5217\u7a7a\u95f44 NulA\u4e0eColA\u4e4b\u95f4\u7684\u5bf9\u6bd45  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":388,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-387","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/387","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=387"}],"version-history":[{"count":8,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/387\/revisions"}],"predecessor-version":[{"id":396,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/387\/revisions\/396"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/388"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=387"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=387"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}