{"id":1137310,"date":"2025-01-08T21:47:03","date_gmt":"2025-01-08T13:47:03","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1137310.html"},"modified":"2025-01-08T21:47:05","modified_gmt":"2025-01-08T13:47:05","slug":"python%e4%b8%adnumpy%e5%a6%82%e4%bd%95%e5%86%990%e8%a1%8c%e5%88%97%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1137310.html","title":{"rendered":"python\u4e2dnumpy\u5982\u4f55\u51990\u884c\u5217\u5f0f"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25101143\/34470bf7-6125-443b-b3a8-16e9941480a0.webp\" alt=\"python\u4e2dnumpy\u5982\u4f55\u51990\u884c\u5217\u5f0f\" \/><\/p>\n<p><p> <strong>\u5728Python\u4e2d\uff0c\u4f7f\u7528NumPy\u5e93\u53ef\u4ee5\u5f88\u65b9\u4fbf\u5730\u8ba1\u7b97\u77e9\u9635\u7684\u884c\u5217\u5f0f\u3002\u8981\u8ba1\u7b97\u4e00\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\u5e76\u786e\u4fdd\u5176\u4e3a0\uff0c\u53ef\u4ee5\u901a\u8fc7\u521b\u5efa\u4e00\u4e2a\u7279\u5b9a\u7684\u77e9\u9635\uff0c\u8fd9\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e3a0\u3002<\/strong> \u4e00\u79cd\u5e38\u89c1\u7684\u65b9\u6cd5\u662f\u521b\u5efa\u4e00\u4e2a\u884c\u6216\u5217\u5b8c\u5168\u4e3a\u96f6\u7684\u77e9\u9635\uff0c\u6216\u521b\u5efa\u4e00\u4e2a\u884c\u4e0e\u53e6\u4e00\u884c\u7ebf\u6027\u76f8\u5173\u7684\u77e9\u9635\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u901a\u8fc7\u8bbe\u7f6e\u67d0\u4e9b\u884c\u6216\u5217\u4f7f\u5176\u76f8\u4e92\u4f9d\u8d56\u6216\u76f8\u540c\uff0c\u5373\u53ef\u786e\u4fdd\u884c\u5217\u5f0f\u4e3a0\u3002\u4e0b\u9762\u6211\u4eec\u8be6\u7ec6\u63a2\u8ba8\u5982\u4f55\u5728Python\u4e2d\u4f7f\u7528NumPy\u521b\u5efa\u548c\u8ba1\u7b970\u884c\u5217\u5f0f\u7684\u77e9\u9635\u3002<\/p>\n<\/p>\n<p><p><strong>\u4e00\u3001\u521b\u5efa\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635<\/strong><\/p>\n<\/p>\n<p><p>\u4e3a\u4e86\u521b\u5efa\u4e00\u4e2a\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u51e0\u79cd\u65b9\u6cd5\uff1a<\/p>\n<\/p>\n<ol>\n<li><strong>\u521b\u5efa\u4e00\u4e2a\u884c\u6216\u5217\u5168\u4e3a\u96f6\u7684\u77e9\u9635<\/strong>\uff1a\u5982\u679c\u77e9\u9635\u4e2d\u7684\u4efb\u4f55\u4e00\u884c\u6216\u4e00\u5217\u5168\u4e3a\u96f6\uff0c\u90a3\u4e48\u8be5\u77e9\u9635\u7684\u884c\u5217\u5f0f\u5fc5\u5b9a\u4e3a\u96f6\u3002<\/li>\n<li><strong>\u521b\u5efa\u5177\u6709\u7ebf\u6027\u76f8\u5173\u884c\u7684\u77e9\u9635<\/strong>\uff1a\u5982\u679c\u77e9\u9635\u4e2d\u7684\u67d0\u4e00\u884c\u662f\u53e6\u4e00\u884c\u7684\u7ebf\u6027\u7ec4\u5408\uff0c\u90a3\u4e48\u8be5\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e5f\u4e3a\u96f6\u3002<\/li>\n<\/ol>\n<p><h3>\u5982\u4f55\u5728Python\u4e2d\u5b9e\u73b0<\/h3>\n<\/p>\n<p><p>\u8ba9\u6211\u4eec\u5148\u901a\u8fc7\u521b\u5efa\u4e00\u4e2a\u7b80\u5355\u7684\u4e8c\u7ef4\u77e9\u9635\u6765\u8bf4\u660e\u5982\u4f55\u4f7f\u7528NumPy\u5e93\u8ba1\u7b97\u884c\u5217\u5f0f\u5e76\u786e\u4fdd\u5b83\u4e3a\u96f6\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<h2><strong>\u521b\u5efa\u4e00\u4e2a3x3\u7684\u77e9\u9635\uff0c\u5176\u4e2d\u7b2c\u4e8c\u884c\u662f\u7b2c\u4e00\u884c\u76842\u500d<\/strong><\/h2>\n<p>matrix = np.array([[1, 2, 3],<\/p>\n<p>                   [2, 4, 6],<\/p>\n<p>                   [7, 8, 9]])<\/p>\n<h2><strong>\u4f7f\u7528NumPy\u8ba1\u7b97\u884c\u5217\u5f0f<\/strong><\/h2>\n<p>det = np.linalg.det(matrix)<\/p>\n<p>print(f&quot;\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\u77e9\u9635\u7684\u7b2c\u4e8c\u884c\u662f\u7b2c\u4e00\u884c\u76842\u500d\uff0c\u56e0\u6b64\u5b83\u4eec\u662f\u7ebf\u6027\u76f8\u5173\u7684\uff0c\u8fd9\u5bfc\u81f4\u884c\u5217\u5f0f\u4e3a\u96f6\u3002<\/p>\n<\/p>\n<p><h3>\u8be6\u7ec6\u63cf\u8ff0\u4e0a\u8ff0\u65b9\u6cd5<\/h3>\n<\/p>\n<p><h4>\u521b\u5efa\u4e00\u4e2a\u884c\u6216\u5217\u5168\u4e3a\u96f6\u7684\u77e9\u9635<\/h4>\n<\/p>\n<p><p>\u8fd9\u79cd\u65b9\u6cd5\u6700\u7b80\u5355\uff0c\u76f4\u63a5\u521b\u5efa\u4e00\u4e2a\u4efb\u610f\u5927\u5c0f\u7684\u77e9\u9635\uff0c\u5e76\u4f7f\u5176\u4e2d\u67d0\u4e00\u884c\u6216\u67d0\u4e00\u5217\u5168\u4e3a\u96f6\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u521b\u5efa\u4e00\u4e2a3x3\u7684\u77e9\u9635\uff0c\u5176\u4e2d\u7b2c\u4e00\u5217\u5168\u4e3a\u96f6<\/p>\n<p>zero_col_matrix = np.array([[0, 2, 3],<\/p>\n<p>                            [0, 4, 6],<\/p>\n<p>                            [0, 8, 9]])<\/p>\n<p>det = np.linalg.det(zero_col_matrix)<\/p>\n<p>print(f&quot;\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7b2c\u4e00\u5217\u5168\u4e3a\u96f6\uff0c\u56e0\u6b64\u884c\u5217\u5f0f\u4e5f\u4e3a\u96f6\u3002<\/p>\n<\/p>\n<p><h4>\u521b\u5efa\u5177\u6709\u7ebf\u6027\u76f8\u5173\u884c\u7684\u77e9\u9635<\/h4>\n<\/p>\n<p><p>\u7ebf\u6027\u76f8\u5173\u7684\u884c\u6216\u5217\u610f\u5473\u7740\u5176\u4e2d\u4e00\u884c\u6216\u4e00\u5217\u53ef\u4ee5\u8868\u793a\u4e3a\u5176\u4ed6\u884c\u6216\u5217\u7684\u7ebf\u6027\u7ec4\u5408\u3002\u6bd4\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u521b\u5efa\u4e00\u4e2a3x3\u7684\u77e9\u9635\uff0c\u5176\u4e2d\u7b2c\u4e09\u884c\u662f\u7b2c\u4e00\u884c\u548c\u7b2c\u4e8c\u884c\u7684\u548c<\/p>\n<p>linear_dep_matrix = np.array([[1, 2, 3],<\/p>\n<p>                              [4, 5, 6],<\/p>\n<p>                              [5, 7, 9]])<\/p>\n<p>det = np.linalg.det(linear_dep_matrix)<\/p>\n<p>print(f&quot;\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7b2c\u4e09\u884c\u662f\u7b2c\u4e00\u884c\u548c\u7b2c\u4e8c\u884c\u7684\u548c\uff0c\u56e0\u6b64\u884c\u5217\u5f0f\u4e3a\u96f6\u3002<\/p>\n<\/p>\n<p><p><strong>\u4e8c\u3001\u8ba1\u7b97\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u7684\u610f\u4e49<\/strong><\/p>\n<\/p>\n<p><p>\u4e86\u89e3\u5982\u4f55\u521b\u5efa\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u662f\u7ebf\u6027\u4ee3\u6570\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u6982\u5ff5\uff0c\u5b83\u5728\u8bb8\u591a\u5e94\u7528\u9886\u57df\u4e2d\u90fd\u6709\u91cd\u8981\u610f\u4e49\u3002\u4f8b\u5982\uff0c\u5728\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u65f6\uff0c\u5982\u679c\u7cfb\u6570\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e3a0\uff0c\u5219\u7cfb\u7edf\u6ca1\u6709\u552f\u4e00\u89e3\uff0c\u8fd9\u610f\u5473\u7740\u65b9\u7a0b\u7ec4\u53ef\u80fd\u65e0\u89e3\u6216\u6709\u65e0\u7a77\u591a\u4e2a\u89e3\u3002<\/p>\n<\/p>\n<p><h3>\u6570\u5b66\u80cc\u666f<\/h3>\n<\/p>\n<p><p>\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u79f0\u4e3a<strong>\u5947\u5f02\u77e9\u9635<\/strong>\u3002\u5947\u5f02\u77e9\u9635\u5728\u8bb8\u591a\u6570\u5b66\u548c\u5de5\u7a0b\u95ee\u9898\u4e2d\u90fd\u6709\u91cd\u8981\u7684\u610f\u4e49\u3002\u5c24\u5176\u5728\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u548c\u6c42\u9006\u77e9\u9635\u65f6\uff0c\u5947\u5f02\u77e9\u9635\u7684\u51fa\u73b0\u4f1a\u5bfc\u81f4\u95ee\u9898\u7684\u590d\u6742\u5316\u3002<\/p>\n<\/p>\n<p><h3>\u5e94\u7528\u9886\u57df<\/h3>\n<\/p>\n<ol>\n<li><strong>\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3<\/strong>\uff1a\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\uff0c\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u610f\u5473\u7740\u7ebf\u6027\u65b9\u7a0b\u7ec4\u6ca1\u6709\u552f\u4e00\u89e3\u3002<\/li>\n<li><strong>\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66<\/strong>\uff1a\u5728\u53d8\u6362\u77e9\u9635\u4e2d\uff0c\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u4f1a\u5bfc\u81f4\u67d0\u4e9b\u53d8\u6362\uff08\u5982\u7f29\u653e\u3001\u65cb\u8f6c\uff09\u4e0d\u53ef\u9006\u3002<\/li>\n<li><strong><a href=\"https:\/\/docs.pingcode.com\/ask\/59192.html\" target=\"_blank\">\u673a\u5668\u5b66\u4e60<\/a>\u548c\u6570\u636e\u5206\u6790<\/strong>\uff1a\u5728\u8fd9\u4e9b\u9886\u57df\u4e2d\uff0c\u77e9\u9635\u8fd0\u7b97\u548c\u6c42\u9006\u662f\u5e38\u89c1\u7684\u64cd\u4f5c\uff0c\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u53ef\u80fd\u5bfc\u81f4\u7b97\u6cd5\u5931\u6548\u3002<\/li>\n<\/ol>\n<p><p><strong>\u4e09\u3001\u5229\u7528NumPy\u521b\u5efa\u4e0d\u540c\u7c7b\u578b\u7684\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635<\/strong><\/p>\n<\/p>\n<p><h3>\u5355\u4f4d\u77e9\u9635\u7684\u53d8\u5f62<\/h3>\n<\/p>\n<p><p>\u5355\u4f4d\u77e9\u9635\u662f\u4e00\u79cd\u5bf9\u89d2\u7ebf\u5143\u7d20\u5168\u4e3a1\uff0c\u5176\u4ed6\u5143\u7d20\u5168\u4e3a0\u7684\u65b9\u9635\u3002\u901a\u8fc7\u4fee\u6539\u5355\u4f4d\u77e9\u9635\u7684\u67d0\u4e9b\u5143\u7d20\uff0c\u53ef\u4ee5\u521b\u5efa\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">identity_matrix = np.eye(3)<\/p>\n<p>identity_matrix[1] = identity_matrix[0]  # \u4f7f\u7b2c\u4e8c\u884c\u7b49\u4e8e\u7b2c\u4e00\u884c<\/p>\n<p>det = np.linalg.det(identity_matrix)<\/p>\n<p>print(f&quot;\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u5c06\u5355\u4f4d\u77e9\u9635\u7684\u7b2c\u4e8c\u884c\u8bbe\u7f6e\u4e3a\u7b2c\u4e00\u884c\u7684\u503c\uff0c\u8fd9\u4f7f\u5f97\u77e9\u9635\u53d8\u5f97\u7ebf\u6027\u76f8\u5173\uff0c\u5176\u884c\u5217\u5f0f\u4e3a0\u3002<\/p>\n<\/p>\n<p><h3>\u9ad8\u7ef4\u77e9\u9635\u7684\u521b\u5efa<\/h3>\n<\/p>\n<p><p>\u4e0d\u4ec5\u4ec5\u662f\u4e8c\u7ef4\u77e9\u9635\uff0c\u9ad8\u7ef4\u77e9\u9635\u4e5f\u53ef\u4ee5\u6309\u7167\u4e0a\u8ff0\u65b9\u6cd5\u521b\u5efa\u3002\u4f8b\u5982\uff0c\u521b\u5efa\u4e00\u4e2a4&#215;4\u7684\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u521b\u5efa\u4e00\u4e2a4x4\u7684\u77e9\u9635\uff0c\u5176\u4e2d\u7b2c\u56db\u884c\u662f\u7b2c\u4e00\u884c\u76843\u500d<\/p>\n<p>large_matrix = np.array([[1, 2, 3, 4],<\/p>\n<p>                         [5, 6, 7, 8],<\/p>\n<p>                         [9, 10, 11, 12],<\/p>\n<p>                         [3, 6, 9, 12]])<\/p>\n<p>det = np.linalg.det(large_matrix)<\/p>\n<p>print(f&quot;\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7b2c\u56db\u884c\u662f\u7b2c\u4e00\u884c\u76843\u500d\uff0c\u56e0\u6b64\u884c\u5217\u5f0f\u4e3a0\u3002<\/p>\n<\/p>\n<p><h3>\u4f7f\u7528\u968f\u673a\u77e9\u9635<\/h3>\n<\/p>\n<p><p>\u6709\u65f6\uff0c\u6211\u4eec\u53ef\u80fd\u9700\u8981\u4e00\u4e2a\u968f\u673a\u751f\u6210\u7684\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u3002\u8fd9\u53ef\u4ee5\u901a\u8fc7\u751f\u6210\u968f\u673a\u77e9\u9635\u5e76\u4fee\u6539\u5176\u67d0\u4e9b\u884c\u6216\u5217\u6765\u5b9e\u73b0\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u521b\u5efa\u4e00\u4e2a\u968f\u673a\u76844x4\u77e9\u9635<\/p>\n<p>random_matrix = np.random.rand(4, 4)<\/p>\n<h2><strong>\u4f7f\u7b2c\u4e09\u884c\u7b49\u4e8e\u7b2c\u4e00\u884c<\/strong><\/h2>\n<p>random_matrix[2] = random_matrix[0]<\/p>\n<p>det = np.linalg.det(random_matrix)<\/p>\n<p>print(f&quot;\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6211\u4eec\u751f\u6210\u4e86\u4e00\u4e2a\u968f\u673a\u76844&#215;4\u77e9\u9635\uff0c\u5e76\u5c06\u7b2c\u4e09\u884c\u8bbe\u7f6e\u4e3a\u7b2c\u4e00\u884c\u7684\u503c\uff0c\u4ee5\u786e\u4fdd\u884c\u5217\u5f0f\u4e3a0\u3002<\/p>\n<\/p>\n<p><p><strong>\u56db\u3001\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u7684\u6848\u4f8b<\/strong><\/p>\n<\/p>\n<p><h3>\u6848\u4f8b\u4e00\uff1a\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u7684\u591a\u91cd\u5171\u7ebf\u6027\u95ee\u9898<\/h3>\n<\/p>\n<p><p>\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u7ebf\u6027\u56de\u5f52\u6a21\u578b\u4e2d\uff0c\u591a\u91cd\u5171\u7ebf\u6027\u662f\u6307\u81ea\u53d8\u91cf\u4e4b\u95f4\u9ad8\u5ea6\u76f8\u5173\u7684\u95ee\u9898\u3002\u5982\u679c\u8bbe\u8ba1\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e3a0\uff08\u6216\u63a5\u8fd10\uff09\uff0c\u5219\u56de\u5f52\u6a21\u578b\u7684\u89e3\u4e0d\u7a33\u5b9a\u6216\u65e0\u6cd5\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u521b\u5efa\u4e00\u4e2a\u8bbe\u8ba1\u77e9\u9635\uff0c\u5176\u4e2d\u4e00\u5217\u662f\u53e6\u4e00\u5217\u7684\u7ebf\u6027\u7ec4\u5408<\/p>\n<p>X = np.array([[1, 2],<\/p>\n<p>              [3, 6],<\/p>\n<p>              [4, 8]])<\/p>\n<h2><strong>\u8ba1\u7b97\u8bbe\u8ba1\u77e9\u9635\u7684\u884c\u5217\u5f0f<\/strong><\/h2>\n<p>det = np.linalg.det(X.T @ X)<\/p>\n<p>print(f&quot;\u8bbe\u8ba1\u77e9\u9635\u7684\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u8bbe\u8ba1\u77e9\u9635\u7684\u7b2c\u4e8c\u5217\u662f\u7b2c\u4e00\u5217\u76842\u500d\uff0c\u56e0\u6b64\u5176\u884c\u5217\u5f0f\u4e3a0\uff0c\u8fd9\u8bf4\u660e\u5b58\u5728\u591a\u91cd\u5171\u7ebf\u6027\u95ee\u9898\u3002<\/p>\n<\/p>\n<p><h3>\u6848\u4f8b\u4e8c\uff1a\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\u7684\u6295\u5f71\u77e9\u9635<\/h3>\n<\/p>\n<p><p>\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\uff0c\u6295\u5f71\u77e9\u9635\u7528\u4e8e\u5c06\u4e09\u7ef4\u7269\u4f53\u6295\u5f71\u5230\u4e8c\u7ef4\u5e73\u9762\u3002\u5982\u679c\u6295\u5f71\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e3a0\uff0c\u5219\u6295\u5f71\u64cd\u4f5c\u4e0d\u53ef\u9006\uff0c\u53ef\u80fd\u4f1a\u5bfc\u81f4\u6e32\u67d3\u95ee\u9898\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u521b\u5efa\u4e00\u4e2a\u6295\u5f71\u77e9\u9635\uff0c\u5176\u4e2d\u4e00\u884c\u662f\u53e6\u4e00\u884c\u7684\u7ebf\u6027\u7ec4\u5408<\/p>\n<p>projection_matrix = np.array([[1, 0, 0, 0],<\/p>\n<p>                              [0, 1, 0, 0],<\/p>\n<p>                              [0, 0, 0, 0],<\/p>\n<p>                              [0, 0, 0, 0]])<\/p>\n<h2><strong>\u8ba1\u7b97\u6295\u5f71\u77e9\u9635\u7684\u884c\u5217\u5f0f<\/strong><\/h2>\n<p>det = np.linalg.det(projection_matrix)<\/p>\n<p>print(f&quot;\u6295\u5f71\u77e9\u9635\u7684\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u6295\u5f71\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u548c\u7b2c\u56db\u884c\u5168\u4e3a\u96f6\uff0c\u56e0\u6b64\u884c\u5217\u5f0f\u4e3a0\uff0c\u8fd9\u53ef\u80fd\u4f1a\u5bfc\u81f4\u6295\u5f71\u64cd\u4f5c\u4e0d\u53ef\u9006\u3002<\/p>\n<\/p>\n<p><h3>\u6848\u4f8b\u4e09\uff1a\u5de5\u7a0b\u4f18\u5316\u4e2d\u7684\u7ea6\u675f\u77e9\u9635<\/h3>\n<\/p>\n<p><p>\u5728\u5de5\u7a0b\u4f18\u5316\u95ee\u9898\u4e2d\uff0c\u7ea6\u675f\u77e9\u9635\u7528\u4e8e\u5b9a\u4e49\u7cfb\u7edf\u7684\u7ea6\u675f\u6761\u4ef6\u3002\u5982\u679c\u7ea6\u675f\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4e3a0\uff0c\u5219\u7cfb\u7edf\u7684\u7ea6\u675f\u53ef\u80fd\u5b58\u5728\u5197\u4f59\u6216\u4e0d\u4e00\u81f4\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u521b\u5efa\u4e00\u4e2a\u7ea6\u675f\u77e9\u9635\uff0c\u5176\u4e2d\u4e00\u884c\u662f\u53e6\u4e00\u884c\u7684\u7ebf\u6027\u7ec4\u5408<\/p>\n<p>constr<a href=\"https:\/\/docs.pingcode.com\/blog\/59162.html\" target=\"_blank\">AI<\/a>nt_matrix = np.array([[1, 2, 3],<\/p>\n<p>                              [4, 5, 6],<\/p>\n<p>                              [2, 4, 6]])<\/p>\n<h2><strong>\u8ba1\u7b97\u7ea6\u675f\u77e9\u9635\u7684\u884c\u5217\u5f0f<\/strong><\/h2>\n<p>det = np.linalg.det(constraint_matrix)<\/p>\n<p>print(f&quot;\u7ea6\u675f\u77e9\u9635\u7684\u884c\u5217\u5f0f\u7684\u503c\u4e3a: {det}&quot;)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7ea6\u675f\u77e9\u9635\u7684\u7b2c\u4e09\u884c\u662f\u7b2c\u4e00\u884c\u76842\u500d\uff0c\u56e0\u6b64\u884c\u5217\u5f0f\u4e3a0\uff0c\u8fd9\u8bf4\u660e\u7ea6\u675f\u6761\u4ef6\u5b58\u5728\u5197\u4f59\u3002<\/p>\n<\/p>\n<p><p><strong>\u4e94\u3001\u603b\u7ed3<\/strong><\/p>\n<\/p>\n<p><p>\u901a\u8fc7\u672c\u6587\u7684\u8be6\u7ec6\u4ecb\u7ecd\uff0c\u60a8\u5e94\u8be5\u4e86\u89e3\u4e86\u5982\u4f55\u5728Python\u4e2d\u4f7f\u7528NumPy\u5e93\u521b\u5efa\u548c\u8ba1\u7b97\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u3002<strong>\u521b\u5efa\u884c\u6216\u5217\u5168\u4e3a\u96f6\u7684\u77e9\u9635\u3001\u521b\u5efa\u5177\u6709\u7ebf\u6027\u76f8\u5173\u884c\u7684\u77e9\u9635<\/strong>\uff0c\u4ee5\u53ca\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u5982\u4f55\u5904\u7406\u8fd9\u4e9b\u77e9\u9635\u7684\u95ee\u9898\u3002\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u5728\u8bb8\u591a\u6570\u5b66\u548c\u5de5\u7a0b\u95ee\u9898\u4e2d\u90fd\u6709\u91cd\u8981\u7684\u5e94\u7528\u548c\u610f\u4e49\uff0c\u7406\u89e3\u5982\u4f55\u521b\u5efa\u548c\u5904\u7406\u8fd9\u4e9b\u77e9\u9635\u5c06\u5e2e\u52a9\u60a8\u5728\u5404\u79cd\u590d\u6742\u95ee\u9898\u4e2d\u627e\u5230\u89e3\u51b3\u65b9\u6848\u3002\u65e0\u8bba\u662f\u5728\u7ebf\u6027\u4ee3\u6570\u3001\u673a\u5668\u5b66\u4e60\u3001\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u8fd8\u662f\u5de5\u7a0b\u4f18\u5316\u4e2d\uff0c\u884c\u5217\u5f0f\u4e3a0\u7684\u77e9\u9635\u90fd\u662f\u4e00\u4e2a\u5173\u952e\u6982\u5ff5\uff0c\u638c\u63e1\u5b83\u5c06\u4f7f\u60a8\u5728\u76f8\u5173\u9886\u57df\u4e2d\u66f4\u52a0\u5f97\u5fc3\u5e94\u624b\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u5728Python\u4e2d\uff0c\u5982\u4f55\u4f7f\u7528NumPy\u8ba1\u7b97\u884c\u5217\u5f0f\uff1f<\/strong><br \/>\u4f7f\u7528NumPy\u7684<code>numpy.linalg.det()<\/code>\u51fd\u6570\u53ef\u4ee5\u8ba1\u7b97\u6570\u7ec4\u7684\u884c\u5217\u5f0f\u3002\u786e\u4fdd\u8f93\u5165\u7684\u662f\u4e00\u4e2a\u65b9\u9635\uff08\u5373\u884c\u6570\u4e0e\u5217\u6570\u76f8\u540c\uff09\uff0c\u7136\u540e\u8c03\u7528\u8be5\u51fd\u6570\u5373\u53ef\u83b7\u5f97\u884c\u5217\u5f0f\u7684\u503c\u3002\u4f8b\u5982\uff0c<code>det = np.linalg.det(np.array([[1, 2], [3, 4]]))<\/code>\u4f1a\u8fd4\u56de\u77e9\u9635\u7684\u884c\u5217\u5f0f\u3002<\/p>\n<p><strong>\u5982\u4f55\u521b\u5efa\u4e00\u4e2a\u5177\u6709\u96f6\u884c\u5217\u5f0f\u7684\u77e9\u9635\uff1f<\/strong><br \/>\u8981\u521b\u5efa\u4e00\u4e2a\u96f6\u884c\u5217\u5f0f\u7684\u77e9\u9635\uff0c\u53ef\u4ee5\u786e\u4fdd\u77e9\u9635\u7684\u884c\u6216\u5217\u4e4b\u95f4\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\u3002\u4f8b\u5982\uff0c\u77e9\u9635<code>[[1, 2], [2, 4]]<\/code>\u7684\u884c\u5217\u5f0f\u4e3a\u96f6\uff0c\u56e0\u4e3a\u7b2c\u4e8c\u884c\u662f\u7b2c\u4e00\u884c\u7684\u4e24\u500d\u3002\u5728NumPy\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528<code>np.array()<\/code>\u51fd\u6570\u8f7b\u677e\u521b\u5efa\u8fd9\u6837\u7684\u77e9\u9635\u3002<\/p>\n<p><strong>\u662f\u5426\u53ef\u4ee5\u4f7f\u7528NumPy\u4e2d\u7684\u5176\u4ed6\u65b9\u6cd5\u68c0\u67e5\u77e9\u9635\u662f\u5426\u5177\u6709\u96f6\u884c\u5217\u5f0f\uff1f<\/strong><br \/>\u662f\u7684\uff0c\u9664\u4e86\u76f4\u63a5\u8ba1\u7b97\u884c\u5217\u5f0f\u5916\uff0c\u8fd8\u53ef\u4ee5\u901a\u8fc7\u68c0\u67e5\u77e9\u9635\u7684\u79e9\u6765\u5224\u65ad\u5176\u884c\u5217\u5f0f\u662f\u5426\u4e3a\u96f6\u3002\u4f7f\u7528<code>numpy.linalg.matrix_rank()<\/code>\u51fd\u6570\u53ef\u4ee5\u786e\u5b9a\u77e9\u9635\u7684\u79e9\uff0c\u5982\u679c\u79e9\u5c0f\u4e8e\u77e9\u9635\u7684\u7ef4\u6570\uff0c\u5219\u884c\u5217\u5f0f\u4e3a\u96f6\u3002\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u66f4\u9ad8\u6548\u5730\u5904\u7406\u5927\u578b\u77e9\u9635\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\uff0c\u4f7f\u7528NumPy\u5e93\u53ef\u4ee5\u5f88\u65b9\u4fbf\u5730\u8ba1\u7b97\u77e9\u9635\u7684\u884c\u5217\u5f0f\u3002\u8981\u8ba1\u7b97\u4e00\u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f\u5e76\u786e\u4fdd\u5176\u4e3a0\uff0c\u53ef\u4ee5\u901a\u8fc7\u521b [&hellip;]","protected":false},"author":3,"featured_media":1137314,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1137310"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1137310"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1137310\/revisions"}],"predecessor-version":[{"id":1137315,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1137310\/revisions\/1137315"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1137314"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1137310"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1137310"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1137310"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}