\u7ed3\u679c C \u7684\u7b2c i \u884c\u7b2c j \u5217 = A \u7684\u7b2c i \u884c \u4e0e B \u7684\u7b2c j \u5217 \u7684\u70b9\u79ef<\/li>\n<\/ul>\n\u4f8b\u5b50<\/h4>\n
A = [ 1 2 ] B = [ 5 6 ]
\n [ 3 4 ] [ 7 8 ]<\/p>\n
A \u662f 2\u00d72，B \u662f 2\u00d72，\u7ed3\u679c C \u662f 2\u00d72\u3002<\/p>\n
\u7b97 C(0,0)：A \u7b2c 1 \u884c (1,2) \u00b7 B \u7b2c 1 \u5217 (5,7) = 1\u00d75 + 2\u00d77 = 19<\/p>\n
\u7b97 C(0,1)：A \u7b2c 1 \u884c (1,2) \u00b7 B \u7b2c 2 \u5217 (6,8) = 1\u00d76 + 2\u00d78 = 22<\/p>\n
\u7b97 C(1,0)：A \u7b2c 2 \u884c (3,4) \u00b7 B \u7b2c 1 \u5217 (5,7) = 3\u00d75 + 4\u00d77 = 43<\/p>\n
\u7b97 C(1,1)：A \u7b2c 2 \u884c (3,4) \u00b7 B \u7b2c 2 \u5217 (6,8) = 3\u00d76 + 4\u00d78 = 50<\/p>\n
C = [ 19 22 ]
\n [ 43 50 ]<\/p>\n
\u77e9\u9635 \u00d7 \u5411\u91cf<\/h4>\n
\u5411\u91cf\u662f"\u53ea\u6709\u4e00\u5217\u7684\u77e9\u9635"，\u6240\u4ee5\u77e9\u9635\u4e58\u5411\u91cf\u662f\u77e9\u9635\u4e58\u6cd5\u7684\u7279\u6b8a\u60c5\u51b5：<\/p>\n
[ 1 2 ] [ 1 ] [ 1\u00d71 + 2\u00d71 ] [ 3 ]
\n[ 3 4 ] \u00d7 [ 1 ] = [ 3\u00d71 + 4\u00d71 ] = [ 7 ]<\/p>\n
\u77e9\u9635\u4e58\u5411\u91cf = \u5bf9\u5411\u91cf\u505a\u4e00\u6b21"\u53d8\u6362"（\u7b2c 21 \u7ae0\u4f1a\u5c55\u5f00，\u8fd9\u662f\u7406\u89e3\u51e0\u4f55\u7684\u5173\u952e）\u3002<\/p>\n
\u5173\u952e\u6027\u8d28：\u4e0d\u6ee1\u8db3\u4ea4\u6362\u5f8b！<\/h4>\n
\u77e9\u9635\u4e58\u6cd5\u4e0d\u6ee1\u8db3\u4ea4\u6362\u5f8b：A\u00d7B \u2260 B\u00d7A（\u5927\u591a\u6570\u60c5\u51b5\u4e0b）\u3002<\/p>\n
\u800c\u4e14\u987a\u5e8f\u5f71\u54cd\u5c3a\u5bf8：2\u00d73 \u4e58 3\u00d74 \u53ef\u4ee5（\u5f97 2\u00d74），\u4f46 3\u00d74 \u4e58 2\u00d73 \u4e0d\u884c（\u5217\u6570\u4e0d\u7b49\u4e8e\u884c\u6570）\u3002<\/p>\n
\u8bb0\u5fc6：\u77e9\u9635\u4e58\u6cd5"\u5de6\u77e9\u9635\u7684\u5217 = \u53f3\u77e9\u9635\u7684\u884c"\u624d\u80fd\u4e58；\u7ed3\u679c\u5c3a\u5bf8 = \u201c\u5de6\u884c \u00d7 \u53f3\u5217\u201d\u3002<\/p>\n
17.6 \u5728 Eigen \u91cc\u505a\u77e9\u9635\u8fd0\u7b97<\/h3>\n
#<\/span>include<\/span> <Eigen\/Dense><\/span><\/span>
\n#<\/span>include<\/span> <iostream><\/span><\/span><\/p>\nint<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
\n Eigen::<\/span>Matrix2d A,<\/span> B;<\/span>
\n A <<<\/span> 1<\/span>,<\/span> 2<\/span>,<\/span>
\n 3<\/span>,<\/span> 4<\/span>;<\/span>
\n B <<<\/span> 5<\/span>,<\/span> 6<\/span>,<\/span>
\n 7<\/span>,<\/span> 8<\/span>;<\/span><\/p>\n std::<\/span>cout <<<\/span> "A + B =\\\\n"<\/span> <<<\/span> A +<\/span> B <<<\/span> "\\\\n\\\\n"<\/span>;<\/span> \/\/ \u5bf9\u5e94\u76f8\u52a0<\/span>
\n std::<\/span>cout <<<\/span> "2 * A =\\\\n"<\/span> <<<\/span> 2<\/span> *<\/span> A <<<\/span> "\\\\n\\\\n"<\/span>;<\/span> \/\/ \u6570\u4e58<\/span>
\n std::<\/span>cout <<<\/span> "A * B =\\\\n"<\/span> <<<\/span> A *<\/span> B <<<\/span> "\\\\n\\\\n"<\/span>;<\/span> \/\/ \u77e9\u9635\u4e58\u6cd5<\/span>
\n std::<\/span>cout <<<\/span> "A^T =\\\\n"<\/span> <<<\/span> A.<\/span>transpose<\/span>(<\/span>)<\/span> <<<\/span> "\\\\n\\\\n"<\/span>;<\/span> \/\/ \u8f6c\u7f6e<\/span><\/p>\n Eigen::<\/span>Vector3d u<\/span>(<\/span>1<\/span>,<\/span> 2<\/span>,<\/span> 3<\/span>)<\/span>,<\/span> v<\/span>(<\/span>4<\/span>,<\/span> 5<\/span>,<\/span> 6<\/span>)<\/span>;<\/span>
\n std::<\/span>cout <<<\/span> "\u70b9\u79ef = "<\/span> <<<\/span> u.<\/span>dot<\/span>(<\/span>v)<\/span> <<<\/span> "\\\\n"<\/span>;<\/span> \/\/ 32<\/span><\/p>\n return<\/span> 0<\/span>;<\/span>
\n}<\/span><\/p>\n\u5b58\u6210 ch17.cpp，\u6309\u9644\u5f55 C.3 \u7f16\u8bd1\u8fd0\u884c，\u5b9e\u9645\u8f93\u51fa：<\/p>\n
A + B =
\n 6 8
\n10 12<\/p>\n
2 * A =
\n2 4
\n6 8<\/p>\n
A * B =
\n19 22
\n43 50<\/p>\n
A^T =
\n1 3
\n2 4<\/p>\n
\u70b9\u79ef = 32<\/p>\n
A * B \u5f97\u5230 19 22 \/ 43 50，\u6b63\u597d\u7b49\u4e8e\u4f60\u4e0a\u9762\u624b\u7b97\u7684\u7ed3\u679c\u2014\u2014\u77e9\u9635\u4e58\u6cd5\u7684\u7b97\u6cd5\u548c\u4ee3\u7801\u662f\u4e00\u4e00\u5bf9\u5e94\u7684\u3002\u4f60\u53ef\u4ee5\u987a\u624b\u52a0\u4e00\u53e5 std::cout << B * A << "\\\\n";，\u770b\u5230 B * A \u662f 23 34 \/ 31 46，\u548c A * B \u4e0d\u540c，\u4ea4\u6362\u5f8b\u4e0d\u6210\u7acb\u8fd9\u4ef6\u4e8b\u5c31\u4eb2\u773c\u786e\u8ba4\u4e86\u3002<\/p>\n
\u6ce8\u610f Eigen \u7684 *：A * B \u662f\u77e9\u9635\u4e58\u6cd5（\u4e0d\u662f\u9010\u5143\u7d20\u4e58）\u3002\u60f3\u9010\u5143\u7d20\u76f8\u4e58\u8981\u7528 .array()（\u7b2c 27 \u7ae0）\u3002\u8fd9\u662f\u65b0\u624b\u6700\u5bb9\u6613\u641e\u9519\u7684\u5730\u65b9\u3002<\/p>\n
17.7 \u5c0f\u7ed3<\/h3>\n\n- \u52a0\u51cf：\u5bf9\u5e94\u5143\u7d20\u76f8\u52a0\u51cf（\u5c3a\u5bf8\u8981\u76f8\u540c）\u3002<\/li>\n
- \u6570\u4e58：\u6bcf\u4e2a\u5143\u7d20\u4e58\u6807\u91cf\u3002<\/li>\n
- \u8f6c\u7f6e：\u884c\u5217\u4e92\u6362\u3002<\/li>\n
- \u70b9\u79ef：\u5bf9\u5e94\u5206\u91cf\u76f8\u4e58\u6c42\u548c\u3002<\/li>\n
- \u77e9\u9635\u4e58\u6cd5：\u5de6\u77e9\u9635\u5217\u6570 = \u53f3\u77e9\u9635\u884c\u6570，\u7ed3\u679c(i,j) = \u5de6 i \u884c\u70b9\u4e58\u53f3 j \u5217；\u4e0d\u6ee1\u8db3\u4ea4\u6362\u5f8b\u3002<\/li>\n<\/ul>\n
\u4e0b\u4e00\u7ae0，\u7528\u77e9\u9635\u8868\u793a\u548c\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u2014\u2014\u77e9\u9635\u6700\u91cd\u8981\u7684\u5e94\u7528\u3002<\/p>\n
\n\u7ec3\u4e60\u9898<\/h4>\n
- \u8ba1\u7b97\u4e24\u4e2a 2\u00d72 \u77e9\u9635\u7684\u52a0\u51cf\u3002<\/li>\n
- \u624b\u7b97\u77e9\u9635\u4e58\u6cd5：A=[1 2; 3 4]，B=[5 6; 7 8]，\u6c42 A\u00d7B \u548c B\u00d7A，\u9a8c\u8bc1\u4ea4\u6362\u5f8b\u4e0d\u6210\u7acb\u3002<\/li>\n
- \u8ba1\u7b97\u5411\u91cf (1,2,3) \u548c (4,5,6) \u7684\u70b9\u79ef\u3002<\/li>\n
- \u6c42\u77e9\u9635 [1 2 3; 4 5 6] \u7684\u8f6c\u7f6e\u3002<\/li>\n
- \u5224\u65ad：2\u00d73 \u77e9\u9635\u80fd\u548c 3\u00d72 \u77e9\u9635\u76f8\u4e58\u5417？\u7ed3\u679c\u662f\u591a\u5c11\u5c3a\u5bf8？<\/li>\n","protected":false},"excerpt":{"rendered":"
\u5b66\u4f1a\u77e9\u9635\u7684\\”\u56db\u5219\u8fd0\u7b97\\”\u3002\u5176\u4e2d\u77e9\u9635\u4e58\u6cd5\u662f\u6700\u91cd\u8981\u4e5f\u6700\u5bb9\u6613\u641e\u6df7\u7684，\u672c\u7ae0\u91cd\u70b9\u8bb2\u900f\u300217.1 \u77e9\u9635\u52a0\u51cf：\u5bf9\u5e94\u5143\u7d20\u76f8\u52a0\u51cf
\n\u4e24\u4e2a\u5c3a\u5bf8\u76f8\u540c\u7684\u77e9\u9635，\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u76f8\u52a0\u51cf：
\n[ 1 2 ] [ 5 6 ] [ 15 26 ] [ 6 8 ]
\n[ 3 4 ] [ 7 8 ] [ 37 48 ] [ 10 12 ]\u89c4\u5219：\u540c\u884c\u540c\u5217\u7684\u5143\u7d20\u76f8\u52a0\u3002\u51cf\u6cd5\u540c\u7406\u3002
\n17.2 \u6570\u4e58：\u6bcf\u4e2a\u5143\u7d20\u90fd\u4e58\u4e00\u4e2a\u6570
\n\u4e00\u4e2a\u6807<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55],"topic":[],"class_list":["post-113434","post","type-post","status-publish","format-standard","hentry","category-server","tag-c"],"yoast_head":"\n
\u7b2c 17 \u7ae0 \u00b7 \u77e9\u9635\u8fd0\u7b97 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/113434.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u7b2c 17 \u7ae0 \u00b7 \u77e9\u9635\u8fd0\u7b97 - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u5b66\u4f1a\u77e9\u9635\u7684"\u56db\u5219\u8fd0\u7b97"\u3002\u5176\u4e2d\u77e9\u9635\u4e58\u6cd5\u662f\u6700\u91cd\u8981\u4e5f\u6700\u5bb9\u6613\u641e\u6df7\u7684，\u672c\u7ae0\u91cd\u70b9\u8bb2\u900f\u300217.1 \u77e9\u9635\u52a0\u51cf：\u5bf9\u5e94\u5143\u7d20\u76f8\u52a0\u51cf \u4e24\u4e2a\u5c3a\u5bf8\u76f8\u540c\u7684\u77e9\u9635，\u5bf9\u5e94\u4f4d\u7f6e\u7684\u5143\u7d20\u76f8\u52a0\u51cf： [ 1 2 ] [ 5 6 ] [ 15 26 ] [ 6 8 ] [ 3 4 ] [ 7 8 ] [ 37 48 ] [ 10 12 ]\u89c4\u5219：\u540c\u884c\u540c\u5217\u7684\u5143\u7d20\u76f8\u52a0\u3002\u51cf\u6cd5\u540c\u7406\u3002 17.2 \u6570\u4e58：\u6bcf\u4e2a\u5143\u7d20\u90fd\u4e58\u4e00\u4e2a\u6570 \u4e00\u4e2a\u6807\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/113434.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-10-06T02:49:42+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/113434.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/113434.html\",\"name\":\"\u7b2c 17 \u7ae0 \u00b7 \u77e9\u9635\u8fd0\u7b97 - 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