{"id":33447,"date":"2022-03-08T13:00:51","date_gmt":"2022-03-08T13:00:51","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33447"},"modified":"2025-07-23T11:05:20","modified_gmt":"2025-07-23T11:05:20","slug":"%e3%83%a6%e3%83%bc%e3%82%af%e3%83%aa%e3%83%83%e3%83%89%e7%a9%ba%e9%96%93-rn","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e3%83%a6%e3%83%bc%e3%82%af%e3%83%aa%e3%83%83%e3%83%89%e7%a9%ba%e9%96%93-rn\/","title":{"rendered":"\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 Rn"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">{\\mathbb{R}^n}<\/span><\/span><\/h1>\n<p style=\"text-align:center;\" dir=\"ltr\"><em>\u3053\u306e\u8b1b\u7fa9\u3067\u306f\u3001<strong>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span><\/strong>\u3001\u305d\u306e\u4ee3\u6570\u7684\u69cb\u9020\u304a\u3088\u3073\u8ddd\u96e2\u306b\u95a2\u3059\u308b\u6027\u8cea\u306b\u3064\u3044\u3066\u63a2\u7a76\u3057\u307e\u3059\u3002\u30d9\u30af\u30c8\u30eb\u6f14\u7b97\u3001<strong>\u5185\u7a4d<\/strong>\u3001<strong>\u30ce\u30eb\u30e0<\/strong>\u3001<strong>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2<\/strong>\u306a\u3069\u3001\u5e7e\u4f55\u5b66\u304a\u3088\u3073\u89e3\u6790\u306b\u304a\u3051\u308b\u57fa\u672c\u7684\u6982\u5ff5\u3092\u5b66\u3073\u307e\u3059\u3002\u660e\u78ba\u306a\u8aac\u660e\u3068\u76f4\u611f\u7684\u306a\u4f8b\u3092\u901a\u3058\u3066\u3001\u591a\u6b21\u5143\u7a7a\u9593\u3092\u6570\u5b66\u7684\u306b\u3069\u306e\u3088\u3046\u306b\u30e2\u30c7\u30eb\u5316\u3059\u308b\u304b\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/em><\/p>\n<p style=\"text-align:center;\" dir=\"ltr\">\n<strong>\u5b66\u7fd2\u76ee\u6a19\uff1a<\/strong><br \/>\n\u3053\u306e\u8b1b\u7fa9\u306e\u7d42\u4e86\u6642\u306b\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a\n<\/p>\n<ol>\n<li><strong>\u5b9a\u7fa9\u3059\u308b<\/strong> \u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u3068\u305d\u306e\u57fa\u672c\u7684\u6027\u8cea\u3002<\/li>\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u30d9\u30af\u30c8\u30eb\u69cb\u9020\u3068\u57fa\u672c\u6f14\u7b97\u306b\u3088\u308b\u6027\u8cea\u3002<\/li>\n<li><strong>\u9069\u7528\u3059\u308b<\/strong> \u5185\u7a4d\u3092\u7528\u3044\u3066\u30d9\u30af\u30c8\u30eb\u9593\u306e\u89d2\u5ea6\u3084\u5c04\u5f71\u3092\u8a08\u7b97\u3059\u308b\u3002<\/li>\n<li><strong>\u8a3c\u660e\u3059\u308b<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306b\u304a\u3051\u308b\u5185\u7a4d\u306e\u4ee3\u6570\u7684\u304a\u3088\u3073\u8ddd\u96e2\u7684\u6027\u8cea\u3002<\/li>\n<li><strong>\u5229\u7528\u3059\u308b<\/strong> \u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30ce\u30eb\u30e0\u306b\u3088\u308a\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u6c42\u3081\u308b\u3002<\/li>\n<li><strong>\u8a08\u7b97\u3059\u308b<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306b\u304a\u3051\u308b2\u70b9\u9593\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3068\u305d\u306e\u5e7e\u4f55\u5b66\u7684\u610f\u5473\u3092\u5206\u6790\u3059\u308b\u3002<\/li>\n<li><strong>\u78ba\u8a8d\u3059\u308b<\/strong> \u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f\u3084\u4e09\u89d2\u4e0d\u7b49\u5f0f\u306e\u3088\u3046\u306a\u57fa\u672c\u7684\u4e0d\u7b49\u5f0f\u306e\u59a5\u5f53\u6027\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\" dir=\"ltr\"><strong>\u76ee\u6b21<\/strong><br \/>\n<a href=\"#1\">\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span><\/a><br \/>\n<a href=\"#2\">\u5185\u7a4d<\/a><br \/>\n<a href=\"#3\">\u30ce\u30eb\u30e0\u3068\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2<\/a><br \/>\n<a href=\"#4\">\u7d50\u8ad6<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/mV-G69l9LtI\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span><\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=mV-G69l9LtI&#038;t=123s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u3053\u306e\u6642\u70b9\u306b\u5230\u9054\u3059\u308b\u524d\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span><\/span> \u306e\u6027\u8cea\u3001\u3042\u308b\u3044\u306f\u5e73\u9762 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^2,<\/span><\/span> \u3084\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^3<\/span><\/span> \u306b\u6163\u308c\u89aa\u3057\u3093\u3067\u3044\u305f\u3053\u3068\u3067\u3057\u3087\u3046\u3002<\/span><\/strong><\/a> \u305d\u308c\u3089\u306e\u6982\u5ff5\u306f\u3059\u3079\u3066\u3001\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u3092\u7406\u89e3\u3059\u308b\u4e0a\u3067\u6709\u7528\u3067\u3059\u3002\u307e\u305a\u4f55\u3088\u308a\u3082\u3001\u96c6\u5408 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n = \\{\\vec{x} = (x_1, \\cdots, x_n) | x_1, \\cdots, x_n \\in \\mathbb{R}\\}<\/span><\/span> \u306b\u901a\u5e38\u306e\u30d9\u30af\u30c8\u30eb\u306e\u52a0\u6cd5\u3068\u30b9\u30ab\u30e9\u30fc\u500d\u3092\u5099\u3048\u305f\u3082\u306e\u306f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3042\u308a\u3001\u3053\u3053\u3067\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u57fa\u672c\u7684\u306a\u6f14\u7b97\u3092\u8a73\u3057\u304f\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306b\u304a\u3051\u308b\u57fa\u672c\u6f14\u7b97<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=mV-G69l9LtI&#038;t=232s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u30d9\u30af\u30c8\u30eb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}=(x_1, \\cdots, x_n), \\vec{y}=(y_1, \\cdots, y_n)<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306b\u5c5e\u3057\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha<\/span><\/span> \u304c\u4efb\u610f\u306e\u5b9f\u6570\u30b9\u30ab\u30e9\u30fc\u3067\u3042\u308b\u3068\u304d\u3001<\/span><\/strong><\/a>\u4ee5\u4e0b\u306b\u793a\u3059\u3088\u3046\u306b\u3001<strong>\u30d9\u30af\u30c8\u30eb\u306e\u52a0\u7b97<\/strong>\u3068<strong>\u30b9\u30ab\u30e9\u30fc\u500d<\/strong>\u306e\u6f14\u7b97\u304c\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p><strong>\u30d9\u30af\u30c8\u30eb\u306e\u52a0\u7b97\uff1a<\/strong> \u30d9\u30af\u30c8\u30eb\u306e\u52a0\u7b97\u306f\u6b21\u306e\u95a2\u6570\u306b\u3088\u3063\u3066\u8a18\u8ff0\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rcrl} +:&amp; \\mathbb{R}^n \\times \\mathbb{R}^n &amp; \\longrightarrow &amp; \\mathbb{R}^n \\\\ &amp; (\\vec{x},\\vec{y}) &amp; \\longmapsto &amp; \\vec{x}+\\vec{y} = (x_1+y_1, \\cdots, x_n + y_n) \\end{array} <\/span><\/span><\/p>\n<p><strong>\u30b9\u30ab\u30e9\u30fc\u500d\uff1a<\/strong> \u30b9\u30ab\u30e9\u30fc\u500d\u306f\u6b21\u306e\u95a2\u6570\u306b\u3088\u3063\u3066\u8a18\u8ff0\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{rcrl} ():&amp; \\mathbb{R} \\times \\mathbb{R}^n &amp; \\longrightarrow &amp; \\mathbb{R}^n \\\\ &amp; (\\alpha,\\vec{x}) &amp; \\longmapsto &amp; (\\alpha\\vec{x}) = (\\alpha x_1, \\cdots, \\alpha x_n) \\end{array} <\/span>\n<h3><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u3057\u3066\u306e\u6027\u8cea<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=mV-G69l9LtI&#038;t=428s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u4e0a\u8a18\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u6f14\u7b97\u3092\u5099\u3048\u305f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306f\u3001<\/span><\/strong><\/a><strong>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<\/strong>\u3067\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u305d\u306e\u52a0\u6cd5\u304a\u3088\u3073\u30b9\u30ab\u30e9\u30fc\u500d\u306e\u6f14\u7b97\u304c\u4ee5\u4e0b\u306b\u793a\u3059\u6027\u8cea\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u304b\u3089\u3067\u3059\uff1a<\/p>\n<p>\u307e\u305a\u3001<strong>\u53ef\u63db\u6027<\/strong>\u3068<strong>\u7d50\u5408\u6027<\/strong>\u306e\u6027\u8cea\u304c\u3042\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\vec{x} + \\vec{y} = \\vec{y} + \\vec{x}  \\\\ \\vec{x} + (\\vec{y}  + \\vec{z}) = (\\vec{x} + \\vec{y})  + \\vec{z}  \\\\ (\\alpha \\beta) \\vec{x}  = \\alpha (\\beta  \\vec{x}) = \\beta (\\alpha  \\vec{x}) = (\\beta\\alpha) \\vec{x}\n\n<\/span>\n<p><strong>\u30b9\u30ab\u30e9\u30fc\u306e\u52a0\u7b97\u306f\u30b9\u30ab\u30e9\u30fc\u500d\u306b\u95a2\u3057\u3066\u5206\u914d\u3055\u308c\u3001\u30d9\u30af\u30c8\u30eb\u52a0\u7b97\u3082\u30b9\u30ab\u30e9\u30fc\u500d\u306b\u95a2\u3057\u3066\u5206\u914d\u3055\u308c\u307e\u3059\u3002<\/strong>\u3059\u306a\u308f\u3061\u3001\u4ee5\u4e0b\u306e\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> (\\alpha + \\beta) \\vec{x} = \\alpha\\vec{x} + \\beta\\vec{x} \\\\ \\alpha(\\vec{x} + \\vec{y}) = \\alpha\\vec{x} + \\alpha\\vec{y} <\/span>\n<p><strong>\u52a0\u6cd5\u5358\u4f4d\u5143<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">\\vec{0}=(0,\\cdots, 0)<\/span> \u304c\u5b58\u5728\u3057\u3001\u6b21\u306e\u6027\u8cea\u3092\u6e80\u305f\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vec{x} + \\vec{0} = \\vec{x} <\/span>\n<p>\u30b9\u30ab\u30e9\u30fc\u500d\u306b\u304a\u3044\u3066\u306f <strong>\u4e57\u6cd5\u5358\u4f4d\u5143<\/strong> \u304c\u5b58\u5728\u3057\u3001<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> 1 \\vec{x} = \\vec{x} <\/span>\n<p>\u3059\u3079\u3066\u306e\u30d9\u30af\u30c8\u30eb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}\\in\\mathbb{R}^n<\/span><\/span> \u306b\u5bfe\u3057\u3066\u3001<strong>\u52a0\u6cd5\u9006\u5143<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-\\vec{x}<\/span><\/span> \u304c\u5b58\u5728\u3057\u3001\u6b21\u306e\u6027\u8cea\u3092\u6e80\u305f\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\vec{x} + -\\vec{x} = \\vec{0} <\/span><\/span><\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/HL85aSpHdsI\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u5185\u7a4d\uff08\u30b9\u30ab\u30e9\u30fc\u7a4d\uff09<\/h2>\n<p>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u69cb\u9020\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u305d\u3053\u306b\u306f\u30d9\u30af\u30c8\u30eb\u540c\u58eb\u306e\u7a4d\u304c\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u901a\u5e38\u306e\u5b9f\u6570\u306e\u3088\u3046\u306b\u30d9\u30af\u30c8\u30eb\u540c\u58eb\u3092\u300c\u639b\u3051\u308b\u300d\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u30d9\u30af\u30c8\u30eb\u9593\u306b\u5b9a\u7fa9\u53ef\u80fd\u306a\u6f14\u7b97\u304c\u3042\u308a\u3001\u305d\u306e\u4e00\u3064\u304c <strong>\u5185\u7a4d\uff08\u30b9\u30ab\u30e9\u30fc\u7a4d\uff09<\/strong> \u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=HL85aSpHdsI&#038;t=349s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u5185\u7a4d\uff08\u30b9\u30ab\u30e9\u30fc\u7a4d\uff09\u3068\u30b9\u30ab\u30e9\u30fc\u500d\u3092\u6df7\u540c\u3057\u3066\u306f\u306a\u308a\u307e\u305b\u3093\u3002<\/span><\/strong><\/a> \u524d\u8005\u306f2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u7a4d\u3067\u3042\u308a\u3001\u7d50\u679c\u306f\u30b9\u30ab\u30e9\u30fc\uff08\u5b9f\u6570\uff09\u306b\u306a\u308a\u307e\u3059\u3002\u5f8c\u8005\u306f\u30b9\u30ab\u30e9\u30fc\u3068\u30d9\u30af\u30c8\u30eb\u306e\u7a4d\u3067\u3042\u308a\u3001\u7d50\u679c\u306f\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u3053\u3053\u3067\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306b\u5c5e\u3059\u308b2\u3064\u306e\u30d9\u30af\u30c8\u30eb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}=(x_1, \\cdots, x_n)<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{y}=(y_1, \\cdots, y_n)<\/span><\/span> \u3092\u8003\u3048\u307e\u3059\u3002\u3053\u308c\u3089\u3092\u7528\u3044\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{y}<\/span><\/span> \u306e\u5185\u7a4d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}\\cdot\\vec{y}<\/span><\/span> \u306f\u6b21\u306e\u5f0f\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}\\cdot\\vec{y} =\\displaystyle \\sum_{i=1}^n x_i y_i = x_1y_1 + \\cdots x_ny_n<\/span>\n<p>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306b\u304a\u3051\u308b\u5185\u7a4d\u306e\u8868\u73fe\u306b\u306f\u3055\u307e\u3056\u307e\u306a\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u4e00\u3064\u306f\u4e0a\u8a18\u306e\u5f0f\u3067\u3042\u308a\u3001\u3082\u3046\u4e00\u3064\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u57fa\u5e95\u3068<strong>\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u7e2e\u7d04\u8a18\u6cd5<\/strong>\u3092\u7528\u3044\u308b\u65b9\u6cd5\u3067\u3059\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{\\hat{e}_i\\}_{i=\\overline{1,n}}<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u57fa\u5e95\uff08\u901a\u5e38\u306f\u6a19\u6e96\u57fa\u5e95\uff09\u3068\u3059\u308b\u3068\u3001\u30d9\u30af\u30c8\u30eb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{y}<\/span><\/span> \u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}=\\displaystyle\\sum_{i=1}^n x_i\\hat{e}_i = x_1\\hat{e}_1 + \\cdots x_n\\hat{e}_n<\/span>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{y}=\\displaystyle\\sum_{i=1}^n y_i\\hat{e}_i = y_1\\hat{e}_1 + \\cdots y_n\\hat{e}_n<\/span>\n<p>\u3053\u3053\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u4fc2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_i<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y_i<\/span><\/span> \u304c\u7a7a\u9593\u306e\u57fa\u5e95\u306b\u5bfe\u3059\u308b\u3082\u306e\u3067\u3042\u308b\u3053\u3068\u304c\u660e\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h3>\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u548c\u8a18\u6cd5<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=HL85aSpHdsI&#038;t=518s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u548c\u8a18\u6cd5<\/span><\/strong><\/a> \u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u8868\u8a18\u5168\u822c\u304a\u3088\u3073\u7279\u306b\u5185\u7a4d\u306e\u8868\u73fe\u3092\u7c21\u6f54\u306b\u3059\u308b\u305f\u3081\u306e\u65b9\u6cd5\u3067\u3059\u3002\u524d\u306e2\u3064\u306e\u5f0f\u3092\u898b\u3066\u307f\u308b\u3068\u3001\u6dfb\u5b57 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">i<\/span><\/span> \u304c\u30d9\u30af\u30c8\u30eb\u306e\u4fc2\u6570\u3068\u57fa\u5e95\u30d9\u30af\u30c8\u30eb\u306e\u4e21\u65b9\u306b\u73fe\u308c\u3066\u3044\u307e\u3059\u3002\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306b\u3088\u308c\u3070\u3001\u6dfb\u5b57\u304c\u7e70\u308a\u8fd4\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u308c\u306f\u548c\u3092\u610f\u5473\u3057\u3066\u3044\u308b\u3068\u307f\u306a\u305b\u308b\u305f\u3081\u3001\u6b21\u306e\u3088\u3046\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}=  x_i\\hat{e}_i<\/span>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{y}= y_i\\hat{e}_i <\/span>\n<p>\u3053\u306e\u8a18\u6cd5\u3092\u7528\u3044\u308b\u3068\u3001\u5185\u7a4d\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u73fe\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}\\cdot\\vec{y} = x_i\\hat{e}_i \\cdot y_i\\hat{e}_i = x_iy_i \\underbrace{(\\hat{e}_i \\cdot \\hat{e}_i)}_{=1} = x_iy_i  <\/span>\n<p>\u3053\u306e\u6700\u5f8c\u306e\u7b49\u5f0f\u3067\u306f\u3001\u6a19\u6e96\u57fa\u5e95\u3092\u7528\u3044\u3066\u3044\u308b\u3053\u3068\u304c\u4eee\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p>\n<h3>\u5185\u7a4d\u306b\u95a2\u3059\u308b\u4ed6\u306e\u8a18\u6cd5<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=HL85aSpHdsI&#038;t=825s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u30d9\u30af\u30c8\u30eb\u304a\u3088\u3073\u305d\u306e\u6f14\u7b97\u306e\u8a18\u6cd5\u306f\u6587\u8108\u306b\u3088\u3063\u3066\u7570\u306a\u308b\u3053\u3068\u304c\u591a\u304f\u3001<\/span><\/strong><\/a>\u3053\u306e\u7bc0\u306e\u5192\u982d\u3067\u7528\u3044\u305f\u3082\u306e\u306f\u3001\u5fae\u7a4d\u5206\u306e\u6587\u8108\u3067\u6700\u3082\u3088\u304f\u898b\u3089\u308c\u308b\u4e00\u822c\u7684\u306a\u5f62\u5f0f\u3067\u3059\u3002\u4e00\u65b9\u3001\u7dda\u5f62\u4ee3\u6570\u5b66\u3067\u306f\u30d9\u30af\u30c8\u30eb\u3068\u5171\u30d9\u30af\u30c8\u30eb\u3092\u533a\u5225\u3057\u3066\u8a18\u8ff0\u3059\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\uff1a<\/p>\n<p>\u3053\u3053\u3067\u300c\u30d9\u30af\u30c8\u30eb\u300d\u3068\u306f\u300c\u5217\u30d9\u30af\u30c8\u30eb\u300d\u3092\u610f\u5473\u3057\u3001\u884c\u5217\u8868\u73fe\u3067\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304b\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha^i = \\left( \\begin{array}{c}\\alpha_1 \\\\ \\vdots \\\\ \\alpha_n \\end{array} \\right)  <\/span>\n<p>\u4e00\u65b9\u3001\u300c\u5171\u30d9\u30af\u30c8\u30eb\u300d\u3068\u306f\u300c\u884c\u30d9\u30af\u30c8\u30eb\u300d\u3092\u610f\u5473\u3057\u3001\u884c\u5217\u8868\u73fe\u3067\u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304b\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\beta_i = \\left( \\beta_1 \\; \\cdots \\; \\beta_n  \\right)  <\/span>\n<p>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}=(x_1,\\cdots,x_n)<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{y}=(y_1,\\cdots,y_n)<\/span><\/span> \u306e\u5185\u7a4d\u306f\u3001\u300c\u5171\u30d9\u30af\u30c8\u30eb\u300d<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">x_i<\/span><\/span> \u3068\u30d9\u30af\u30c8\u30eb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">y^i<\/span><\/span> \u306e\u884c\u5217\u7a4d\u3068\u3057\u3066\u89e3\u91c8\u3055\u308c\u3001\u6b21\u306e\u3088\u3046\u306a\u5b9f\u6570\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left( x_1 \\; \\cdots \\; x_n  \\right) \\left( \\begin{array}{c}y_1 \\\\ \\vdots \\\\ y_n \\end{array} \\right)  = x_iy^i  <\/span>\n<p>\u3053\u306e\u6700\u5f8c\u306e\u7b49\u5f0f\u306b\u3082\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u548c\u8a18\u6cd5\u304c\u518d\u3073\u767b\u5834\u3057\u307e\u3059\u3002\u6dfb\u5b57\u306e\u7e70\u308a\u8fd4\u3057\u304c\u3001\u7d50\u679c\u304c\u548c\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u30d9\u30af\u30c8\u30eb\u3068\u5171\u30d9\u30af\u30c8\u30eb\u3092\u6dfb\u5b57\u3068\u4e0a\u4ed8\u304d\u8a18\u53f7\u3067\u533a\u5225\u3059\u308b\u8a18\u6cd5\u306f\u300c\u5171\u5909\u8a18\u6cd5\u300d\u307e\u305f\u306f\u300c\u30c6\u30f3\u30bd\u30eb\u8a18\u6cd5\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u304a\u308a\u3001\u7279\u6b8a\u76f8\u5bfe\u6027\u7406\u8ad6\u3084\u4e00\u822c\u76f8\u5bfe\u6027\u7406\u8ad6\u306e\u7814\u7a76\u306b\u304a\u3044\u3066\u5e83\u304f\u7528\u3044\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u8a18\u6cd5\u306f\u3001\u4eca\u898b\u3066\u304d\u305f\u5185\u5bb9\u3092\u3055\u3089\u306b\u4e00\u822c\u5316\u3057\u305f\u6982\u5ff5\u3067\u3042\u308b\u30c6\u30f3\u30bd\u30eb\u3092\u6271\u3046\u969b\u306b\u3082\u4fbf\u5229\u3067\u3059\u3002\u3053\u306e\u30c6\u30f3\u30bd\u30eb\u306e\u6982\u5ff5\u306b\u3064\u3044\u3066\u306f\u3001\u5225\u306e\u6a5f\u4f1a\u306b\u8a73\u3057\u304f\u53d6\u308a\u4e0a\u3052\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u91cf\u5b50\u529b\u5b66\u306e\u3088\u3046\u306a\u4ed6\u306e\u5206\u91ce\u3067\u306f\u3001Bra\u2013Ket \u8a18\u6cd5\u304c\u597d\u307e\u308c\u3001\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt; x \\right| =\\left( x_1 \\; \\cdots \\; x_n  \\right) \\\\ \\\\ \\left|y\\right&gt; = \\left( \\begin{array}{c}y_1 \\\\ \\vdots \\\\ y_n \\end{array} \\right)\n\n <\/span>\n<p>\u3053\u306e\u3068\u304d\u3001\u5185\u7a4d\uff08\u30b9\u30ab\u30e9\u30fc\u7a4d\uff09\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\left&lt;x|y\\right&gt;.<\/span><\/span><\/p>\n<h3>\u5185\u7a4d\u306e\u6027\u8cea<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=HL85aSpHdsI&#038;t=1083s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u5185\u7a4d\u306e\u5b9a\u7fa9\u304b\u3089\u306f\u3001\u5c06\u6765\u7684\u306b\u975e\u5e38\u306b\u91cd\u8981\u3068\u306a\u308b\u591a\u304f\u306e\u6027\u8cea\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/strong><\/a><\/p>\n<p>\u5185\u7a4d\u3092\u7528\u3044\u3066\u3001\u6b21\u306e\u3088\u3046\u306a\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tilde{\\omega}(\\vec{x})=\\vec{\\omega} \\cdot \\vec{x} = \\omega_i x^i<\/span><\/span> \u3092\u5b9a\u7fa9\u3059\u308b\u3068\u3001\u3053\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tilde{\\omega}<\/span><\/span> \u3068\u3044\u3046\u95a2\u6570\u306f\u7dda\u5f62\u95a2\u6570\u306e\u3059\u3079\u3066\u306e\u6027\u8cea\u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u5b9f\u969b\u3001\u6b21\u306e\u6027\u8cea\u304c\u7c21\u5358\u306b\u8a3c\u660e\u3067\u304d\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} \\tilde{\\omega}(\\alpha \\vec{x} + \\beta\\vec{y}) = \\alpha \\tilde{\\omega}(\\vec{x}) + \\beta\\tilde{\\omega}(\\vec{y}) \\end{array}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u3088\u3046\u306b\u5185\u7a4d\u304b\u3089\u5b9a\u7fa9\u3055\u308c\u308b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tilde{\\omega}<\/span><\/span> \u306e\u3088\u3046\u306a\u5bfe\u8c61\u306f <strong>\u7dda\u5f62\u6c4e\u95a2\u6570<\/strong>\uff08functional lineal\uff09\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3059\u3067\u306b\u77e5\u3063\u3066\u3044\u308b\u3088\u3046\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}<\/span><\/span> \u306f <strong>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u8981\u7d20\u3067\u3042\u308a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\tilde{\\omega}<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e <strong>\u53cc\u5bfe\u7a7a\u9593<\/strong> \u306e\u8981\u7d20\u3067\u3059\u3002<\/p>\n<p>\u3053\u306e\u3053\u3068\u304b\u3089\u3001\u5185\u7a4d\u3068\u7dda\u5f62\u95a2\u6570\u306e\u9593\u306b\u306f\u5bc6\u63a5\u306a\u95a2\u4fc2\u304c\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u5b9f\u969b\u3001\u5185\u7a4d\u306e\u91cd\u8981\u306a\u6027\u8cea\u3092\u307e\u3068\u3081\u305f\u8868\u73fe\u3068\u3057\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8ff0\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a<em><strong>\u300c\u5185\u7a4d\u306f\u53cc\u7dda\u5f62\u30fb\u5bfe\u79f0\u30fb\u6b63\u5b9a\u5024\u30fb\u975e\u9000\u5316\u306a\u5f62\u5f0f\u3067\u3042\u308b\u300d<\/strong><\/em>\u3002\u305d\u308c\u305e\u308c\u306e\u610f\u5473\u3092\u898b\u3066\u3044\u304d\u307e\u3057\u3087\u3046\uff1a<\/p>\n<p><strong>\u5185\u7a4d\u304c\u53cc\u7dda\u5f62\u5f62\u5f0f\u3067\u3042\u308b<\/strong> \u3068\u3044\u3046\u306e\u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x},\\vec{y}<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{z}<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u30d9\u30af\u30c8\u30eb\u3067\u3042\u308a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta \\in \\mathbb{R}<\/span><\/span> \u306e\u3068\u304d\u3001\u6b21\u306e2\u3064\u306e\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u3068\u3044\u3046\u3053\u3068\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} \\vec{x}\\cdot(\\alpha \\vec{y} + \\beta\\vec{z}) = \\alpha (\\vec{x}\\cdot\\vec{y}) + \\beta(\\vec{x}\\cdot\\vec{z}) \\\\ \\\\ (\\alpha \\vec{x} + \\beta\\vec{y})\\cdot\\vec{z} = \\alpha (\\vec{x} \\cdot \\vec{z}) + \\beta(\\vec{y}\\cdot\\vec{z}) \\end{array}<\/span>\n<p><strong>\u5185\u7a4d\u306f\u5bfe\u79f0\u7684<\/strong>\u3067\u3059\u3002\u306a\u305c\u306a\u3089\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\forall(\\vec{x},\\vec{y}\\in\\mathbb{R}^n)(\\vec{x}\\cdot\\vec{y} = \\vec{y}\\cdot\\vec{x})<\/span>\n<p>\u307e\u305f\u3001<strong>\u6b63\u5b9a\u5024<\/strong>\u3067\u3059\u3002\u306a\u305c\u306a\u3089\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(\\forall\\vec{x}\\in\\mathbb{R}^n)(\\vec{x}\\cdot\\vec{x} \\geq 0)<\/span>\n<p>\u3055\u3089\u306b\u3001<strong>\u975e\u9000\u5316\u6027\uff08\u30ce\u30f3\u30c7\u30b8\u30a7\u30cd\u30ec\u30fc\u30c8\uff09<\/strong>\u3092\u6301\u3061\u307e\u3059\u3002\u306a\u305c\u306a\u3089\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}\\cdot\\vec{x} = 0 \\leftrightarrow \\vec{x}=\\vec{0}<\/span>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/vTFqDBEyU4Y\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u30ce\u30eb\u30e0\u3068\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2<\/h2>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=vTFqDBEyU4Y&#038;t=174s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u30ce\u30eb\u30e0\u3068\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\uff08\u9577\u3055\uff09\u3092\u6e2c\u308b\u65b9\u6cd5\u3067\u3059\u3002<\/span><\/strong><\/a>\u30ce\u30eb\u30e0\u3092\u5099\u3048\u305f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306f\u3001<strong>\u30ce\u30eb\u30e0\u7a7a\u9593\uff08Normed Vector Space\uff09<\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x},\\vec{y}\\in\\mathbb{R}^n<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lambda\\in\\mathbb{R}<\/span><\/span> \u306e\u3068\u304d\u3001\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Norm( . )<\/span><\/span> \u304c\u4ee5\u4e0b\u306e\u6027\u8cea\u3092\u6e80\u305f\u305b\u3070\u3001\u305d\u308c\u306f\u30ce\u30eb\u30e0\u3068\u547c\u3070\u308c\u307e\u3059\uff1a<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Norm(\\vec{x})\\geq 0<\/span><\/span>\uff08\u975e\u8ca0\u6027\uff09<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Norm(\\vec{x}) = 0 \\leftrightarrow \\vec{x}=\\vec{0}<\/span><\/span>\uff08\u96f6\u30d9\u30af\u30c8\u30eb\u3068\u306e\u540c\u5024\u6027\uff09<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Norm(\\lambda\\vec{x}) = |\\lambda| Norm(\\vec{x})<\/span><\/span>\uff08\u30b9\u30ab\u30e9\u30fc\u500d\u306b\u5bfe\u3059\u308b\u6589\u6b21\u6027\uff09<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Norm(\\vec{x} + \\vec{y}) \\leq Norm(\\vec{x}) + Norm(\\vec{y})<\/span><\/span>\uff08\u4e09\u89d2\u4e0d\u7b49\u5f0f\uff09<\/li>\n<\/ol>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=vTFqDBEyU4Y&#038;t=350s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u5185\u7a4d\u306e\u91cd\u8981\u306a\u5074\u9762\u306e\u4e00\u3064\u306f\u3001<\/span><\/strong><\/a>\u305d\u308c\u304c\u76f4\u611f\u7684\u306b\u7406\u89e3\u3067\u304d\u308b2\u70b9\u9593\u306e\u8ddd\u96e2\u3068\u3044\u3046\u6982\u5ff5\u3092\u6570\u5b66\u7684\u306b\u5b9a\u7fa9\u3059\u308b\u305f\u3081\u306b\u975e\u5e38\u306b\u6709\u7528\u3067\u3042\u308b\u3068\u3044\u3046\u70b9\u3067\u3059\u3002\u4efb\u610f\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}\\in\\mathbb{R}^n<\/span><\/span> \u306b\u5bfe\u3057\u3066\u3001<strong>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30ce\u30eb\u30e0<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\|\\vec{x}\\|<\/span><\/span> \u304c\u6b21\u306e\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\|\\vec{x}\\| = \\sqrt{\\vec{x}\\cdot\\vec{x}}<\/span>\n<p>\u3053\u306e\u3053\u3068\u304b\u3089\u3001<strong>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30ce\u30eb\u30e0\u306f\u5185\u7a4d\u306b\u3088\u3063\u3066\u8a98\u5c0e\u3055\u308c\u308b\u30ce\u30eb\u30e0<\/strong>\u3067\u3042\u308b\u3068\u8a00\u3048\u307e\u3059\u3002<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=vTFqDBEyU4Y&#038;t=846s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u8ddd\u96e2\uff08\u307e\u305f\u306f\u8ddd\u96e2\u95a2\u6570\u3001\u30e1\u30c8\u30ea\u30c3\u30af\uff09<\/span><\/strong><\/a>\u3068\u306f\u3001\u300c\u96c6\u5408\u5185\u306e2\u8981\u7d20\u9593\u306e\u9694\u305f\u308a\uff08\u8ddd\u96e2\uff09\u300d\u3092\u5b9a\u91cf\u5316\u3059\u308b\u95a2\u6570\u306e\u3053\u3068\u3067\u3059\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}, \\vec{y}, \\vec{z}\\in\\mathbb{R}^n<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lambda\\in\\mathbb{R}<\/span><\/span> \u306b\u5bfe\u3057\u3066\u3001\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Dist( . )<\/span><\/span> \u304c\u4ee5\u4e0b\u306e\u6027\u8cea\u3092\u6e80\u305f\u305b\u3070\u3001\u305d\u308c\u306f\u8ddd\u96e2\uff08\u30e1\u30c8\u30ea\u30c3\u30af\uff09\u3068\u547c\u3070\u308c\u307e\u3059\uff1a<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Dist(\\vec{x},\\vec{y})=0 \\leftrightarrow \\vec{x}=\\vec{y}<\/span><\/span>\uff08\u8b58\u5225\u6027\uff09<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Dist(\\vec{x},\\vec{y})=Dist(\\vec{y},\\vec{x})\\geq 0<\/span><\/span>\uff08\u5bfe\u79f0\u6027\u3068\u975e\u8ca0\u6027\uff09<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Dist(\\vec{x},\\vec{z})\\leq Dist(\\vec{x},\\vec{y}) + Dist(\\vec{y},\\vec{z})<\/span><\/span>\uff08\u4e09\u89d2\u4e0d\u7b49\u5f0f\uff09<\/li>\n<\/ol>\n<p>\u6700\u5f8c\u306e\u6027\u8cea\u306f<strong>\u4e09\u89d2\u4e0d\u7b49\u5f0f<\/strong>\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u304a\u308a\u3001\u3053\u308c\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u5834\u5408\u3001\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">Dist(.)<\/span><\/span> \u306f\u300c\u64ec\u8ddd\u96e2\u95a2\u6570\u300d\u3042\u308b\u3044\u306f\u300c\u64ec\u30e1\u30c8\u30ea\u30c3\u30af\u300d\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u8ddd\u96e2\u3092\u5099\u3048\u305f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306f\u3001<strong>\u8ddd\u96e2\u7a7a\u9593\uff08\u30e1\u30c8\u30ea\u30c3\u30af\u7a7a\u9593\uff09<\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=vTFqDBEyU4Y&#038;t=1013s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30ce\u30eb\u30e0\u306b\u57fa\u3065\u3044\u3066\u3001<\/span><\/strong><\/a><strong>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2<\/strong>\u304c2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u9593\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x},\\vec{y}\\in\\mathbb{R}^n<\/span><\/span> \u3068\u3044\u30462\u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308b\u3068\u304d\u3001\u3053\u308c\u3089\u306e\u9593\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dist_e(\\vec{x},\\vec{y})<\/span><\/span> \u306f\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dist_e(\\vec{x},\\vec{y}) = \\|\\vec{x} - \\vec{y}\\|<\/span>\n<p>\u3053\u3053\u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}=(x_1,\\cdots,x_n)<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{y}=(y_1,\\cdots, y_n)<\/span><\/span> \u306e\u3068\u304d\u3001\u5185\u7a4d\u3068\u30ce\u30eb\u30e0\u306e\u6027\u8cea\u304b\u3089\u6b21\u306e\u3088\u3046\u306b\u7c21\u5358\u306b\u5c0e\u3051\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">dist_e(\\vec{x},\\vec{y}) = \\sqrt{\\displaystyle \\sum_{i=1}^n (x_i - y_i)^2}<\/span>\n<p>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306b\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u3067\u3001<strong>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593<\/strong> \u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u3053\u306e\u3053\u3068\u304b\u3089\u3001<strong>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u306e\u8ddd\u96e2\uff08\u30e1\u30c8\u30ea\u30c3\u30af\uff09\u306f\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30ce\u30eb\u30e0\u306b\u3088\u3063\u3066\u8a98\u5c0e\u3055\u308c\u308b\u30e1\u30c8\u30ea\u30c3\u30af<\/strong>\u3067\u3042\u308b\u3068\u8a00\u308f\u308c\u307e\u3059\u3002<\/p>\n<h3>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30ce\u30eb\u30e0\u306e\u6027\u8cea<\/h3>\n<p><\/strong>\u672c\u8b1b\u7fa9\u3067\u306f\u7279\u306b\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u3092\u5bfe\u8c61\u3068\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30ce\u30eb\u30e0\u306e\u6027\u8cea\u3092\u78ba\u8a8d\u3057\u3066\u304a\u304f\u3053\u3068\u306f\u6709\u76ca\u3067\u3059\u3002<\/p>\n<h4>\u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=vTFqDBEyU4Y&#038;t=1624s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u3082\u3057 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x},\\vec{y}\\in\\mathbb{R}^n<\/span><\/span> \u306a\u3089\u3070\u3001\u6b21\u306e\u6027\u8cea\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff1a<\/span><\/strong><\/a><\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|\\vec{x}\\cdot\\vec{y}|\\leq \\|\\vec{x}\\|\\|\\vec{y}\\|<\/span>\n<p>\u8a3c\u660e\uff1a<\/p>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\lambda = (\\vec{x}\\cdot\\vec{y})\/\\|\\vec{y}\\|^2<\/span><\/span> \u3068\u304a\u304f\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} 0\\leq \\|\\vec{x} - \\lambda \\vec{y}\\|^2 &amp;= (\\vec{x} - \\lambda\\vec{y}) \\cdot (\\vec{x} - \\lambda\\vec{y}) \\\\ \\\\\n\n\\displaystyle &amp;= \\vec{x}\\cdot\\vec{x} - \\lambda\\vec{x}\\cdot\\vec{y} + \\lambda\\vec{y}\\cdot\\vec{x} + \\lambda^2(\\vec{y}\\cdot\\vec{y})\\\\ \\\\\n\n&amp;= \\|\\vec{x}\\|^2 - 2\\lambda(\\vec{x}\\cdot\\vec{y}) + \\lambda^2 \\|\\vec{y}\\|^2 \\\\ \\\\\n\n\\displaystyle &amp;= \\|\\vec{x}\\|^2 - 2\\left(\\frac{\\vec{x}\\cdot\\vec{y}}{\\|\\vec{y}\\|^2}\\right)(\\vec{x}\\cdot\\vec{y}) + \\left(\\frac{\\vec{x}\\cdot\\vec{y}}{{\\|\\vec{y}\\|^2}}\\right)^2 {\\|\\vec{y}\\|^2}\\\\ \\\\\n\n\\displaystyle &amp;= \\|\\vec{x}\\|^2 - 2\\left(\\frac{(\\vec{x}\\cdot\\vec{y})^2}{\\|\\vec{y}\\|^2}\\right) + \\frac{\\left(\\vec{x}\\cdot\\vec{y}\\right)^2}{\\|\\vec{y}\\|^2}\\\\ \\\\\n\n&amp;= \\|\\vec{x}\\|^2 - \\frac{\\left(\\vec{x}\\cdot\\vec{y}\\right)^2}{\\|\\vec{y}\\|^2} \\end{array}<\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u3088\u3046\u306b\u8a00\u3048\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle 0 \\leq \\|\\vec{x}\\|^2 - \\frac{\\left(\\vec{x}\\cdot\\vec{y}\\right)^2}{\\|\\vec{y}\\|^2} <\/span>\n<p>\u3057\u305f\u304c\u3063\u3066\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\left(\\vec{x}\\cdot\\vec{y}\\right)^2 \\leq \\|\\vec{x}\\|^2 \\|\\vec{y}\\|^2 <\/span>\n<p>\u6700\u5f8c\u306b\u5e73\u65b9\u6839\u3092\u3068\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u793a\u3055\u308c\u307e\u3057\u305f\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> |\\vec{x}\\cdot\\vec{y}| \\leq \\|\\vec{x}\\| \\|\\vec{y}\\|<\/span> \u2b1b<\/p>\n<h4>\u4e09\u89d2\u4e0d\u7b49\u5f0f<\/h4>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=vTFqDBEyU4Y&#038;t=2065s\" rel=\"noopener\" target=\"_blank\"><strong><span style=\"color: #ff0000;\">\u30d9\u30af\u30c8\u30eb <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x},\\vec{y}\\in\\mathbb{R}^n<\/span><\/span> \u306b\u5bfe\u3057\u3066\u3001<\/span><\/strong><\/a>\u6b21\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\|\\vec{x} + \\vec{y}\\| \\leq \\|\\vec{x}\\| + \\|\\vec{y}\\|<\/span>\n<p>\u8a3c\u660e\uff1a<\/p>\n<p>\u307e\u305a\u6b21\u306e\u3053\u3068\u306b\u6ce8\u76ee\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl} \\|\\vec{x} + \\vec{y}\\|^2 &amp;= (\\vec{x} + \\vec{y})\\cdot(\\vec{x} + \\vec{y}) \\\\ \\\\ &amp;=\\|\\vec{x}\\|^2 + 2(\\vec{x}\\cdot\\vec{y}) + \\|\\vec{y}\\|^2 \\end{array}<\/span>\n<p>\u6b21\u306e\u4e0d\u7b49\u5f0f\u304c\u6210\u308a\u7acb\u3064\u306e\u3067\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vec{x}\\cdot\\vec{y}\\leq |\\vec{x}\\cdot\\vec{y}| \\leq \\|\\vec{x}\\|\\vec{y}\\|<\/span>\n<p>\u6b21\u306e\u3088\u3046\u306b\u66f8\u3051\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\|\\vec{x} + \\vec{y}\\|^2 &amp;\\leq  \\|\\vec{x}\\|^2 + 2\\|\\vec{x}\\|\\|\\vec{y}\\| + \\|\\vec{y}\\|^2 \\\\ \\\\\n\n&amp;\\leq  \\left(\\|\\vec{x}\\|  + \\|\\vec{y}\\| \\right)^2\n\n\\end{array}<\/span>\n<p>\u6700\u5f8c\u306b\u5e73\u65b9\u6839\u3092\u53d6\u308c\u3070\u3001\u6b21\u306e\u3088\u3046\u306b\u8a3c\u660e\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\|\\vec{x} + \\vec{y}\\|\\leq  \\|\\vec{x}\\|  + \\|\\vec{y}\\|<\/span> \u2b1b <\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u7d50\u8ad6<\/h2>\n<p>\u3053\u306e\u8b1b\u7fa9\u3092\u901a\u3058\u3066\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306e\u57fa\u672c\u7684\u6027\u8cea\u306b\u3064\u3044\u3066\u5b66\u3073\u307e\u3057\u305f\u3002\u307e\u305a\u3001\u30d9\u30af\u30c8\u30eb\u306e\u52a0\u7b97\u3084\u5185\u7a4d\u3068\u3044\u3063\u305f\u57fa\u672c\u7684\u306a\u6f14\u7b97\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3067\u3001\u3053\u306e\u7a7a\u9593\u304c\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u7d9a\u3044\u3066\u3001\u5185\u7a4d\u306e\u6982\u5ff5\u3068\u305d\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}^n<\/span><\/span> \u306b\u304a\u3051\u308b\u5e7e\u4f55\u5b66\u7684\u610f\u5473\u3092\u6398\u308a\u4e0b\u3052\u3001\u884c\u5217\u8868\u73fe\u3084\u7dda\u5f62\u95a2\u6570\u3068\u306e\u95a2\u4fc2\u306b\u3082\u6ce8\u76ee\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u3055\u3089\u306b\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u30ce\u30eb\u30e0\u3068\u305d\u308c\u306b\u3088\u3063\u3066\u8a98\u5c0e\u3055\u308c\u308b\u8ddd\u96e2\u306b\u3064\u3044\u3066\u8003\u5bdf\u3057\u3001\u3053\u308c\u3089\u306e\u9053\u5177\u304c\u7a7a\u9593\u5185\u306e\u9577\u3055\u3084\u8ddd\u96e2\u3092\u5b9a\u91cf\u7684\u306b\u6271\u3046\u306e\u306b\u6709\u52b9\u3067\u3042\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3057\u305f\u3002\u307e\u305f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u57fa\u672c\u7684\u306a\u6027\u8cea\u3092\u78ba\u8a8d\u3057\u307e\u3057\u305f\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> |\\vec{x}\\cdot\\vec{y}| \\leq \\|\\vec{x}\\| \\|\\vec{y}\\| <\/span>\n<p>\uff08\u30b3\u30fc\u30b7\u30fc\u30fb\u30b7\u30e5\u30ef\u30eb\u30c4\u306e\u4e0d\u7b49\u5f0f\uff09\u304a\u3088\u3073\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\|\\vec{x} + \\vec{y}\\|\\leq  \\|\\vec{x}\\|  + \\|\\vec{y}\\| <\/span>\n<p>\uff08\u4e09\u89d2\u4e0d\u7b49\u5f0f\uff09\u3053\u308c\u3089\u306f\u3001\u89e3\u6790\u3084\u5e7e\u4f55\u5b66\u306e\u3088\u308a\u9ad8\u5ea6\u306a\u7406\u8ad6\u3092\u5c55\u958b\u3059\u308b\u3046\u3048\u3067\u91cd\u8981\u306a\u57fa\u790e\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 \u3053\u306e\u8b1b\u7fa9\u3067\u306f\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 \u3001\u305d\u306e\u4ee3\u6570\u7684\u69cb\u9020\u304a\u3088\u3073\u8ddd\u96e2\u306b\u95a2\u3059\u308b\u6027\u8cea\u306b\u3064\u3044\u3066\u63a2\u7a76\u3057\u307e\u3059\u3002\u30d9\u30af\u30c8\u30eb\u6f14\u7b97\u3001\u5185\u7a4d\u3001\u30ce\u30eb\u30e0\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u306a\u3069\u3001\u5e7e\u4f55\u5b66\u304a\u3088\u3073\u89e3\u6790\u306b\u304a\u3051\u308b\u57fa\u672c\u7684\u6982\u5ff5\u3092\u5b66\u3073\u307e\u3059\u3002\u660e\u78ba\u306a\u8aac\u660e\u3068\u76f4\u611f\u7684\u306a\u4f8b\u3092\u901a\u3058\u3066\u3001\u591a\u6b21\u5143\u7a7a\u9593\u3092\u6570\u5b66\u7684\u306b\u3069\u306e\u3088\u3046\u306b\u30e2\u30c7\u30eb\u5316\u3059\u308b\u304b\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u5b66\u7fd2\u76ee\u6a19\uff1a \u3053\u306e\u8b1b\u7fa9\u306e\u7d42\u4e86\u6642\u306b\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a \u5b9a\u7fa9\u3059\u308b 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