{"id":9235,"date":"2024-04-04T00:59:35","date_gmt":"2024-04-03T16:59:35","guid":{"rendered":"\/?p=9235"},"modified":"2024-04-04T00:59:35","modified_gmt":"2024-04-03T16:59:35","slug":"%e3%80%90%e6%95%b0%e5%ad%a6%e8%ae%a1%e7%ae%97%e3%80%91%e7%82%b9%e4%b9%98-%e7%82%b9%e7%a7%af-%e5%86%85%e7%a7%af-%e6%95%b0%e9%87%8f%e7%a7%af-%e5%8f%89%e4%b9%98-%e5%a4%96%e7%a7%af-%e5%8f%89%e7%a7%af","status":"publish","type":"post","link":"\/?p=9235","title":{"rendered":"\u3010\u6570\u5b66\u8ba1\u7b97\u3011\u70b9\u4e58\/\u70b9\u79ef\/\u5185\u79ef\/\u6570\u91cf\u79ef\/\u53c9\u4e58\/\u5916\u79ef\/\u53c9\u79ef\/\u5411\u91cf\u79ef"},"content":{"rendered":"<h5>\u5e8f\u8a00<\/h5>\n<ul>\n<li>\u533a\u5206\u4e00\u4e0b\u8fd9\u51e0\u4e2a\u6982\u5ff5<\/li>\n<\/ul>\n<h5>1. \u70b9\u4e58<\/h5>\n<ul>\n<li>\u70b9\u4e58 = \u70b9\u79ef = \u5185\u79ef = \u6570\u91cf\u79ef<\/li>\n<li><strong>dot product<\/strong> = <strong>inner product<\/strong> = <strong>scalar product<\/strong><\/li>\n<li><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005408210.png\" alt=\"image-20240404005408210\" \/> <\/li>\n<li>\u4ece\u4ee3\u6570\u89d2\u5ea6\u770b\uff0c\u70b9\u79ef\u662f\u5bf9\u4e24\u4e2a\u5411\u91cf<strong>\u5bf9\u5e94\u4f4d\u7f6e\u4e0a\u7684\u503c\u76f8\u4e58\u518d\u76f8\u52a0<\/strong>\u7684\u64cd\u4f5c\uff0c\u5176\u7ed3\u679c\u5373\u4e3a\u70b9\u79ef<\/li>\n<\/ul>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005424686.png\" alt=\"image-20240404005424686\" \/><\/p>\n<ul>\n<li><strong>\u70b9\u4e58\u7684\u51e0\u4f55\u610f\u4e49<\/strong>\uff1a\u5411\u91cfb\u5728\u5411\u91cfa\u65b9\u5411\u4e0a\u7684\u6295\u5f71\u4e0e\u5411\u91cfa\u7684\u6a21\u7684\u4e58\u79ef\uff0c\u7528\u6765\u8868\u5f81\u6216\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u95f4\u7684\u5939\u89d2\uff0c\u8868\u5f81\u4e24\u4e2a\u5411\u91cf\u5728\u65b9\u5411\u4e0a\u7684\u76f8\u4f3c\u5ea6\uff0c\u7ed3\u679c\u8d8a\u5927\u8d8a\u76f8\u4f3c<\/li>\n<\/ul>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005439278.png\" alt=\"image-20240404005439278\" \/><\/p>\n<ul>\n<li>\n<p>\u57fa\u4e8e<a href=\"https:\/\/so.csdn.net\/so\/search?q=\u70b9\u4e58&amp;spm=1001.2101.3001.7020\">\u70b9\u4e58<\/a>\u7ed3\u679c\u53ef\u4ee5\u5224\u65ad\u8fd9\u4e24\u4e2a\u5411\u91cf\u662f\u5426\u662f\u540c\u4e00\u65b9\u5411\uff0c\u662f\u5426\u6b63\u4ea4\u5782\u76f4\uff0c\u5177\u4f53\u5bf9\u5e94\u5173\u7cfb\uff1a<\/p>\n<pre><code class=\"language-cpp\"> \u70b9\u4e58 > 0\uff1a\u5411\u91cf\u5939\u89d2\u57280~90\u00b0\u4e4b\u95f4\n \u70b9\u4e58 = 0\uff1a\u6b63\u4ea4\uff0c\u76f8\u4e92\u5782\u76f4\n \u70b9\u4e58 < 0\uff1a\u5939\u89d2\u572890~180\u00b0\u4e4b\u95f4<\/code><\/pre>\n<\/li>\n<li>\n<p>\u516c\u5f0f\u63a8\u5bfc<\/p>\n<pre><code class=\"language-cpp\">1. \u5411\u91cfc = a - b\n2. c^2 = a^2 + b^2 - 2abcos(theta)\n3. (a - b) \u25aa (a - b) = a^2 + b^2 \u2013 2a\u25aab = a^2 + b^2 - 2abcos(theta)<\/code><\/pre>\n<\/li>\n<\/ul>\n<h5>2. \u53c9\u4e58<\/h5>\n<ul>\n<li>\n<p>\u53c9\u4e58 = \u53c9\u79ef = \u5916\u79ef = \u5411\u91cf\u79ef<\/p>\n<\/li>\n<li>\n<p><strong>cross product<\/strong> = <strong>outer product<\/strong><\/p>\n<\/li>\n<li>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005508647.png\" alt=\"image-20240404005508647\" \/> <\/p>\n<\/li>\n<li>\n<p>\u4ece\u4ee3\u6570\u89d2\u5ea6\u8ba1\u7b97\uff1a<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005530297.png\" alt=\"image-20240404005530297\" \/> <\/p>\n<\/li>\n<li>\n<p>\u4ece\u51e0\u4f55\u89d2\u5ea6\u8ba1\u7b97<\/p>\n<ul>\n<li>\u5176\u4e2d<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005616971.png\" alt=\"image-20240404005616971\" \/>\u5206\u522b\u662fx\u8f74\u3001y\u8f74\u3001z\u8f74\u65b9\u5411\u7684\u5355\u4f4d\u5411\u91cf<\/li>\n<li>\u5f53<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005630026.png\" alt=\"image-20240404005630026\" \/>\u7b49\u4e8e0\u7684\u65f6\u5019\uff0c\u5373\u5f97\u5230\u4e8c\u7ef4\u5411\u91cf\u53c9\u4e58\u7684\u7ed3\u679c<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005640544.png\" alt=\"image-20240404005640544\" \/><\/p>\n<ul>\n<li><strong>\u53c9\u4e58\u7684\u51e0\u4f55\u610f\u4e49<\/strong>\uff1a\n<ul>\n<li>\u4e8c\u7ef4\u5411\u91cf\u53c9\u4e58\uff1a\u5411\u91cfa\u548c\u5411\u91cfb\u7684\u53c9\u4e58\u8868\u793a<strong>\u5411\u91cfa\u548cb\u6784\u6210\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef<\/strong><\/li>\n<li>\u4e8c\u7ef4\u5411\u91cf\u53c9\u4e58\uff1a\u5982\u679ca\u6216b\u5176\u4e2d\u4e00\u4e2a\u4e3a\u5355\u4f4d\u5411\u91cf\uff0c\u5219axb\u53c9\u4e58\u7ed3\u679c\u8868\u793a\u4ee5\u5355\u4f4d\u5411\u91cf\u4e3a\u5e95\u7684<strong>\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9ad8<\/strong>\uff0c\u53ef\u4ee5\u6709\u6b63\u8d1f<\/li>\n<li>\u4e09\u7ef4\u5411\u91cf\u53c9\u4e58\uff1a\u5411\u91cfa\u548c\u5411\u91cfb\u7684\u53c9\u4e58\u7ed3\u679c\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u8be5\u5411\u91cf\u5782\u76f4\u4e8e\u5411\u91cfa\u548cb\u7ec4\u6210\u7684\u5e73\u9762\uff0c\u5373<strong>\u5e73\u9762\u7684\u6cd5\u5411\u91cf<\/strong>\uff0c\u65b9\u5411\u9075\u5b88\u53f3\u624b\u5b9a\u5219<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/e8b13152c265407cb599e80d0188a551.png\" alt=\"img\" style=\"zoom:50%;\" \/><\/p>\n<ul>\n<li>\n<p>\u53c9\u79ef\u6709\u4e00\u4e2a\u975e\u5e38\u91cd\u8981\u7684\u6027\u8d28\uff0c\u53ef\u901a\u8fc7\u53c9\u79ef\u7684\u7b26\u53f7\u6765\u5224\u65ad<strong>\u4e24\u5411\u91cf\u7684\u987a\u9006\u65f6\u9488\u5173\u7cfb<\/strong><\/p>\n<pre><code class=\"language-cpp\">P x Q > 0, \u5219\u5411\u91cfP\u5728\u5411\u91cfQ\u7684\u987a\u65f6\u9488\u65b9\u5411\uff1b\nP x Q < 0, \u5219\u5411\u91cfP\u5728\u5411\u91cfQ\u7684\u9006\u65f6\u9488\u65b9\u5411\uff1b\nP x Q = 0\uff0c\u8868\u793aP\u4e0eQ\u5171\u7ebf\uff0c\u53ef\u80fd\u540c\u5411\u4e5f\u53ef\u80fd\u53cd\u5411<\/code><\/pre>\n<\/li>\n<\/ul>\n<h5>3. \u70b9\u4e58 vs \u53c9\u4e58\uff0c\u5bf9\u6bd4\u4e0e\u5e94\u7528<\/h5>\n<ul>\n<li>\u70b9\u4e58\u7684\u7ed3\u679c\u662f<strong>\u6807\u91cf<\/strong>(\u5e38\u7528\u4e8e\u7269\u7406)\/<strong>\u6570\u91cf<\/strong>(\u5e38\u7528\u4e8e\u6570\u5b66)\uff0c\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97<strong>\u5939\u89d2<\/strong>\u548c<strong>\u6295\u5f71<\/strong><\/li>\n<li>\u53c9\u4e58\u7684\u7ed3\u679c\u662f<strong>\u77e2\u91cf<\/strong>(\u5e38\u7528\u4e8e\u7269\u7406)\/<strong>\u5411\u91cf<\/strong>(\u5e38\u7528\u4e8e\u6570\u5b66)\uff0c\u6cd5\u5411\u91cf\u7684\u6a21\u5927\u5c0f\u4e3a<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005713159.png\" alt=\"image-20240404005713159\" \/>\uff0c\u65b9\u5411\u9075\u5b88\u53f3\u624b\u5b9a\u5219<\/li>\n<li>\u5728\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u53c9\u4e58\u7ed3\u679c\u7b49\u4e8e\u5411\u91cfa\u548cb\u6784\u6210\u7684<strong>\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef<\/strong>\uff0c\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\uff1a\u4ee5<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005732990.png\" alt=\"image-20240404005732990\" \/>\u4e3a\u9ad8\uff0c\u4ee5<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/image-20240404005751861.png\" alt=\"image-20240404005751861\" \/>\u4e3a\u5e95\u3002\u5f53a\u662f\u5355\u4f4d\u5411\u91cf\u65f6\uff0c\u8ba1\u7b97b\u7684\u7ec8\u70b9\u5230a\u6240\u5728\u76f4\u7ebf\u7684\u8ddd\u79bb\uff0c\u4e5f\u5c31\u662f<strong>\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9ad8<\/strong><\/li>\n<li>\u901a\u8fc7\u5411\u91cf\u7684\u53c9\u4e58\u751f\u6210\u5782\u76f4\u4e8e\u5411\u91cfa\/b\u7684\u6cd5\u5411\u91cf\uff0c\u4ece\u800c<strong>\u6784\u5efaXYZ\u5750\u6807\u7cfb<\/strong><\/li>\n<li>\u53c9\u4e58\u7684\u7ed3\u679c\u518d\u70b9\u4e58\u53ef\u4ee5\u7528\u6765\u5224\u65ad\u5411\u91cf\/\u7ebf\u6bb5\u662f\u5426\u76f8\u4ea4\uff0c\u5373&quot;\u8de8\u7acb\u5b9e\u9a8c&quot;\uff0c\u89c1\u6587\u7ae0<a href=\"https:\/\/blog.csdn.net\/baidu_35692628\/article\/details\/127201071?spm=1001.2014.3001.5502\">\u5224\u65ad\u4e24\u6761\u7ebf\u6bb5\u662f\u5426\u76f8\u4ea4<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u5e8f\u8a00 \u533a\u5206\u4e00\u4e0b\u8fd9\u51e0\u4e2a\u6982\u5ff5 1. \u70b9\u4e58 \u70b9\u4e58 = \u70b9\u79ef = \u5185\u79ef = \u6570\u91cf\u79ef dot product = inner product =    \u2026 &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[260],"tags":[],"_links":{"self":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9235"}],"collection":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9235"}],"version-history":[{"count":1,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9235\/revisions"}],"predecessor-version":[{"id":9237,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9235\/revisions\/9237"}],"wp:attachment":[{"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9235"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9235"},{"taxonomy":"post_tag","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9235"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}