{"id":4301,"date":"2026-07-28T07:06:20","date_gmt":"2026-07-27T22:06:20","guid":{"rendered":"https:\/\/anagileway.com\/?p=4301"},"modified":"2026-07-28T07:28:19","modified_gmt":"2026-07-27T22:28:19","slug":"matrix-world","status":"publish","type":"post","link":"https:\/\/anagileway.com\/en\/2026\/07\/28\/matrix-world\/","title":{"rendered":"Matrix World"},"content":{"rendered":"<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?ssl=1\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"564\" data-attachment-id=\"4303\" data-permalink=\"https:\/\/anagileway.com\/en\/2026\/07\/28\/matrix-world\/image-61\/\" data-orig-file=\"https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?fit=2190%2C1236&amp;ssl=1\" data-orig-size=\"2190,1236\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;,&quot;alt&quot;:&quot;&quot;}\" data-image-title=\"image\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?fit=1000%2C564&amp;ssl=1\" src=\"https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=1000%2C564&#038;ssl=1\" alt=\"\" class=\"wp-image-4303\" srcset=\"https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=1024%2C578&amp;ssl=1 1024w, https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=768%2C433&amp;ssl=1 768w, https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=1536%2C867&amp;ssl=1 1536w, https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=2048%2C1156&amp;ssl=1 2048w, https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=18%2C10&amp;ssl=1 18w, https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=1200%2C677&amp;ssl=1 1200w, https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?resize=1440%2C813&amp;ssl=1 1440w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u66f8\u3067\u7d39\u4ecb\u3057\u305f\u884c\u5217\u306e\u6027\u8cea\u3084\u5206\u985e\u3092\u307e\u3068\u3081\u305f\u5730\u56f3\u3092\u793a\u3057\u307e\u3059\uff08\u57fa\u790e\u4f53\u3068\u3057\u3066\u5b9f\u6570\u3092\u60f3\u5b9a\u3057\u3066\u3044\u307e\u3059\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6b63\u65b9\u3001\u5bfe\u79f0\u3001\u76f4\u4ea4\u3001\u53ef\u9006\u3001\u7f6e\u63db\u3001\u5bfe\u89d2\u3001\u5c04\u5f71\u3001\u5bfe\u89d2\u5316\u53ef\u80fd\u3001\u306a\u3069\u3001\u591a\u304f\u306e\u884c\u5217\u306e\u30ab\u30c6\u30b4\u30ea\u30fc\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u30d9\u30f3\u56f3\u306f\u3001\u305d\u308c\u3089\u306e\u30ab\u30c6\u30b4\u30ea\u30fc\u306e\u95a2\u4fc2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e0a\u304b\u3089\u4e0b\u3078\u3068\u3001\u56f3\u3092\u305f\u3069\u308a\u306a\u304c\u3089\u8aac\u660e\u3057\u307e\u3059\u3002\u4e3b\u8981\u306a\u884c\u5217\u306e\u7a4d\u5206\u89e3\u3068\u89e3\u8aac\u306e\u7ae0\u756a\u53f7\u3082\u793a\u3057\u3066\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3059\u3079\u3066\u306e $m\\times n$ \u884c\u5217\u306f $A=CR$ \u5206\u89e3\u306b\u3088\u3063\u3066\u30e9\u30f3\u30af\u3092\u6c7a\u5b9a\u3067\u304d\u3001\u307e\u305f\u3001 $A=U \\Sigma V\\transp$ \u3068\u7279\u7570\u5024\u5206\u89e3\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5185\u5074\u306b\u5165\u3063\u3066\u3001<strong>\u6b63\u65b9\u884c\u5217<\/strong>\u306f$m=n$\u306e\u5834\u5408\u3067\u3042\u308a\u3001\u3059\u3079\u3066\u306e\u6b63\u65b9\u884c\u5217\u306f<strong>\u53ef\u9006<\/strong>\u304b<strong>\u4e0d\u53ef\u9006<\/strong>\u304b\u306b\u5206\u304b\u308c\u307e\u3059\u3002\u3053\u306e\u5206\u5c90\u7dda\u304c\u4e2d\u592e\u306b\u5f15\u304b\u308c\u305f\u70b9\u7dda\u3067\u3059\u3002\u3053\u306e\u5224\u5b9a\u306f\u3001\u300c $LU$ \u5206\u89e3\u306b\u3088\u3063\u3066 $U$ \u306b\u96f6\u884c\u304c\u5b58\u5728\u3059\u308b\u300d\u3001\u300c $\\det(A) \\ne 0$ \u300d\u3001\u300c\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u304c\u975e\u96f6\u300d\u306a\u3069\u3067\u884c\u3048\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ef\u9006\u884c\u5217\u306f\u3001<strong>\u76f4\u4ea4\u884c\u5217<\/strong> $Q$ \u3068<strong>\u4e0a\u4e09\u89d2\u884c\u5217<\/strong> $R$ \u306e\u7a4d $A=QR$ \u306b\u5206\u89e3\u3067\u304d\u307e\u3059\uff08\u30b0\u30e9\u30e0\u30b7\u30e5\u30df\u30c3\u30c8\u6cd5\uff09\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u307e\u305f\u3001\u6b63\u65b9\u884c\u5217\u306f<strong>\u5bfe\u89d2\u5316\u53ef\u80fd<\/strong>\u306a\u5834\u5408\u3001 $A=X \\Lambda X^{-1}$ \u3068<strong>\u5bfe\u89d2\u884c\u5217<\/strong> $\\Lambda$ \u3068\u53ef\u9006\u884c\u5217 $X$ \u3092\u7528\u3044\u3066\u8868\u3055\u308c\u307e\u3059\u3002 $S\\transp = S$ \u3092\u6e80\u305f\u3059<strong>\u5bfe\u79f0\u884c\u5217<\/strong>\u306f\u3001 $Q\\transp = Q^{-1}$ \u3092\u6e80\u305f\u3059<strong>\u76f4\u4ea4\u884c\u5217<\/strong>\u306b\u3088\u3063\u3066\u5bfe\u89d2\u5316\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u7f6e\u63db\u884c\u5217<\/strong>\u306f\u884c\u3084\u5217\u3092\u5165\u308c\u66ff\u3048\u308b\u884c\u5217\u3067\u3059\u304c\u3001\u3053\u308c\u306f\u76f4\u4ea4\u884c\u5217\u306e\u4ef2\u9593\u3067\u3059\u3002<strong>\u5bfe\u79f0\u884c\u5217<\/strong>\u306e\u4e2d\u306b\u306f<strong>\u6b63\u5b9a\u5024\u884c\u5217<\/strong>\u304c\u3042\u308a\u3001\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u304c\u6b63\u3067\u53ef\u9006\u3067\u3059\u3002\u56fa\u6709\u5024\u3068\u3057\u30660\u3082\u8a8d\u3081\u305f\u5834\u5408\u3001<strong>\u534a\u6b63\u5b9a\u5024\u884c\u5217<\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002<strong>\u5c04\u5f71\u884c\u5217<\/strong>\u306f\u3053\u306e\u4e2d\u306b\u3042\u308a\u3001 $P^2 = P = P\\transp$ \u3092\u6e80\u305f\u3057\u3001\u305d\u306e\u56fa\u6709\u5024\u306f1\u304b0\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5bfe\u79f0\u884c\u5217\u306e\u4e2d\u306b<strong>\u5bfe\u89d2\u884c\u5217<\/strong>\u304c\u4e0d\u53ef\u9006\u3068\u53ef\u9006\u3092\u307e\u305f\u3044\u3067\u4f38\u3073\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u56f3\u306e\u4e2d\u5fc3\u306b<strong>\u5358\u4f4d\u884c\u5217<\/strong> $I$ \u3068 <strong>\u96f6\u884c\u5217<\/strong> $O$ \u304c\u3042\u308a\u307e\u3059\u3002\u3068\u3082\u306b<strong>\u5bfe\u89d2\u884c\u5217<\/strong>\u3067\u3042\u308a<strong>\u5bfe\u79f0\u884c\u5217<\/strong>\u3067\u3042\u308a<strong>\u5c04\u5f71\u884c\u5217<\/strong>\u3067\u3059\u3002\u5358\u4f4d\u884c\u5217\u306f\u3055\u3089\u306b\u53ef\u9006\u3067\u3042\u308a\u3001\u76f4\u4ea4\u3067\u3042\u308a\u3001\u7f6e\u63db\u3067\u3042\u308a\u6b63\u5b9a\u5024\u3067\u3042\u308a\u3001\u3059\u3079\u3066\u306e\u56fa\u6709\u5024\u304c1\u3067\u552f\u4e00\u306e\u53ef\u9006\u306a\u5c04\u5f71\u884c\u5217\u3067\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u672c\u66f8\u3067\u306f\u51fa\u3066\u304d\u307e\u305b\u3093\u3067\u3057\u305f\u304c\u3001\u5bfe\u79f0\u3001\u76f4\u4ea4\u3001\u5c04\u5f71\u3001\u7f6e\u63db\u306a\u3069\u3001\u30e6\u30cb\u30bf\u30ea\u884c\u5217\u306b\u3088\u3063\u3066\u5bfe\u89d2\u5316\u53ef\u80fd\u306a\u884c\u5217\u5168\u4f53\u306e\u547c\u3073\u540d\u304c\u5b58\u5728\u3057\u307e\u3059\u3002<strong>\u6b63\u898f\u884c\u5217<\/strong>\u3068\u547c\u3070\u308c\u3001 $A\\transp A = A A\\transp$ \u3092\u6e80\u305f\u3059\u3053\u3068\u3067\u7279\u5fb4\u3065\u3051\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7279\u306b\u3001\u5b9f\u5bfe\u79f0\u884c\u5217\u306e\u5834\u5408\u306f\u3001\u5b9f\u6570\u306e\u56fa\u6709\u5024\u3068\u5b9f\u76f4\u4ea4\u884c\u5217\u306b\u3088\u3063\u3066\u30b9\u30da\u30af\u30c8\u30eb\u5206\u89e3\u53ef\u80fd\u3067\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u56f3\u306e\u6700\u4e0b\u884c\u306b\u306f\u3001\u3059\u3079\u3066\u306e $A$ \u306b\u5bfe\u3057\u3066\u5b9a\u7fa9\u3067\u304d\u308b $A^+$ \u3068\u3044\u3046<strong>\u64ec\u4f3c\u9006\u884c\u5217<\/strong>\u304c\u914d\u7f6e\u3057\u3066\u3042\u308a\u307e\u3059\u3002\u53ef\u9006\u306a\u6b63\u65b9\u884c\u5217\u306e\u5834\u5408\u3001 $A^+ = A^{-1}$ \u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8a73\u3057\u3044\u89e3\u8aac\uff08\u82f1\u8a9e\uff09\u306f\u3053\u3061\u3089\u3067\u3059\uff0e<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-wp-embed is-provider-an-agile-way wp-block-embed-an-agile-way\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"wp-embedded-content\" data-secret=\"pDnrzFRdeg\"><a href=\"https:\/\/anagileway.com\/en\/2020\/09\/29\/matrix-world-in-linear-algebra-for-everyone\/\">Matrix World in &#8220;Linear Algebra for Everyone&#8221;<\/a><\/blockquote><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; visibility: hidden;\" title=\"\u201cMatrix World in \u201cLinear Algebra for Everyone\u201d\u201d \u2014 an Agile Way\" src=\"https:\/\/anagileway.com\/2020\/09\/29\/matrix-world-in-linear-algebra-for-everyone\/embed\/#?secret=q6Dza3xoQH#?secret=pDnrzFRdeg\" data-secret=\"pDnrzFRdeg\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/x.com\/hiranabe\/status\/2081501463768187345\/photo\/1\"><\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>\u672c\u66f8\u3067\u7d39\u4ecb\u3057\u305f\u884c\u5217\u306e\u6027\u8cea\u3084\u5206\u985e\u3092\u307e\u3068\u3081\u305f\u5730\u56f3\u3092\u793a\u3057\u307e\u3059\uff08\u57fa\u790e\u4f53\u3068\u3057\u3066\u5b9f\u6570\u3092\u60f3\u5b9a\u3057\u3066\u3044\u307e\u3059\uff09\u3002 \u6b63\u65b9\u3001\u5bfe\u79f0\u3001\u76f4\u4ea4 [&hellip;]<\/p>\n","protected":false},"author":24727826,"featured_media":4303,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[782308494,782308495],"class_list":["post-4301","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized","tag-linear-algebra","tag-vla"],"jetpack_publicize_connections":[],"jetpack_likes_enabled":true,"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6Eiku-17n","jetpack-related-posts":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/anagileway.com\/wp-content\/uploads\/2026\/07\/image-2.png?fit=2190%2C1236&ssl=1","_links":{"self":[{"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/posts\/4301","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/users\/24727826"}],"replies":[{"embeddable":true,"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/comments?post=4301"}],"version-history":[{"count":7,"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/posts\/4301\/revisions"}],"predecessor-version":[{"id":4311,"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/posts\/4301\/revisions\/4311"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/media\/4303"}],"wp:attachment":[{"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/media?parent=4301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/categories?post=4301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/anagileway.com\/en\/wp-json\/wp\/v2\/tags?post=4301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}