{"id":101627,"date":"2024-07-16T17:46:05","date_gmt":"2024-07-16T17:46:05","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E7%A9%BA%E9%96%93%E3%81%AE%E6%AC%A1%E5%85%83-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-07-16T17:46:05","modified_gmt":"2024-07-16T17:46:05","slug":"%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E7%A9%BA%E9%96%93%E3%81%AE%E6%AC%A1%E5%85%83-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=101627","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143 &#8211; \u5b9a\u7fa9"},"content":{"rendered":"<div><div><h2>\u5c0e\u5165<\/h2><p>\u7dda\u5f62\u4ee3\u6570\u3067\u306f\u3001<b>\u30cf\u30e1\u30eb\u6b21\u5143<\/b>\u3001\u307e\u305f\u306f\u5358\u306b<b>\u6b21\u5143\u306f\u3001<\/b>\u7269\u4f53<b>K<\/b>\u4e0a\u306e\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<i>E<\/i>\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u305f\u4e0d\u5909\u91cf\u3067\u3059\u3002 <i>E<\/i>\u306e\u6b21\u5143\u306f\u3001\u305d\u306e\u3059\u3079\u3066\u306e\u57fa\u5e95\u306b\u5171\u901a\u306e\u57fa\u6570\u3067\u3059\u3002\u3053\u306e<span><a href=\"https:\/\/science-hub.click\/?p=71097\">\u6570<\/a><\/span>\u306f<span>dim <sub><i>K<\/i><\/sub> ( <i>E<\/i> )<\/span> (\u300c <span><i>K<\/i><\/span>\u4e0a\u306e<span><i>E<\/i><\/span>\u306e\u6b21\u5143\u300d\u3068\u8aad\u307f\u307e\u3059) \u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {\\dim E} $$<\/div> (\u30b9\u30ab\u30e9\u30fc<b>K<\/b>\u306e\u672c\u4f53\u306b\u3064\u3044\u3066\u6df7\u4e71\u304c\u306a\u3044\u5834\u5408) \u307e\u305f\u306f<span>[ <i>E<\/i> : <i>K<\/i> ]<\/span>\u3055\u3048\u3082\u3002 <i>E \u304c<\/i>\u6709\u9650\u306e\u751f\u6210\u90e8\u5206\u3092\u8a8d\u3081\u308b\u5834\u5408\u3001\u305d\u306e<span><a href=\"https:\/\/science-hub.click\/?p=84871\">\u6b21\u5143\u306f<\/a><\/span>\u6709\u9650\u3067\u3042\u308a\u3001 <i>E<\/i>\u306e\u57fa\u5e95\u3092\u69cb\u6210\u3059\u308b\u30d9\u30af\u30c8\u30eb\u306e\u6570\u306b\u5024\u3057\u307e\u3059\u3002<\/p><p>\u3053\u306e<span><a href=\"https:\/\/science-hub.click\/?p=74671\">\u5b9a\u7fa9\u306f<\/a><\/span>\u3001\u4e00\u65b9\u3067\u306f\u4e0d\u5b8c\u5168\u57fa\u5e95<span>\u5b9a\u7406<\/span>\u306e<span>\u5e30\u7d50\u3067<\/span>\u3042\u308b\u57fa\u5e95\u306e\u5b58\u5728\u306b\u57fa\u3065\u3044\u3066\u304a\u308a\u3001\u4ed6\u65b9\u3067\u306f\u540c\u3058\u7a7a\u9593\u306e 2 \u3064\u306e\u57fa\u5e95\u304c\u540c\u3058\u57fa\u6570\u3092\u6301\u3064\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e<span><a href=\"https:\/\/science-hub.click\/?p=20918\">\u6b21\u5143<\/a><\/span>\u5b9a\u7406\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u6b21\u5143\u306f\u3001\u30c9\u30a4\u30c4\u306e<span><a href=\"https:\/\/science-hub.click\/?p=17102\">\u6570\u5b66\u8005<\/a><\/span>\u30b2\u30aa\u30eb\u30b0\u30fb\u30cf\u30fc\u30e1\u30eb\u306b\u3061\u306a\u3093\u3067\u540d\u4ed8\u3051\u3089\u308c\u308b\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u540c\u578b\u5199\u50cf\u306b\u81f3\u308b\u307e\u3067\u3001 <b>K<\/b>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306f\u305d\u306e\u6b21\u5143\u306b\u3088\u3063\u3066\u5206\u985e\u3055\u308c\u307e\u3059\u3002\u7528\u8a9e\u306f\u72ed\u3044\u30b9\u30da\u30fc\u30b9\u306b\u7279\u6709\u306e\u3082\u306e\u3067\u3059\u3002<\/p><ul><li>\u30cc\u30eb\u7a7a\u9593: \u30bc\u30ed\u6b21\u5143\u306e\u7a7a\u9593<i>E \u3092<\/i>\u6307\u5b9a\u3057\u307e\u3059\u3002\u30bc\u30ed<span><a href=\"https:\/\/science-hub.click\/?p=66129\">\u30d9\u30af\u30c8\u30eb<\/a><\/span>\u3092\u552f\u4e00\u306e\u8981\u7d20\u3068\u3057\u3066\u8a8d\u3081\u307e\u3059\u3002<span><a href=\"https:\/\/science-hub.click\/?p=93191\">\u7a7a\u306e<\/a><\/span>\u30d5\u30a1\u30df\u30ea\u30fc\u306f\u6700\u5927\u306e\u81ea\u7531\u30d5\u30a1\u30df\u30ea\u30fc\u3067\u3042\u308a\u3001 <i>E<\/i>\u306e\u4e00\u610f\u306e\u5869\u57fa\u3067\u3042\u308a\u3001\u30d9\u30af\u30c8\u30eb\u3092\u542b\u307f\u307e\u305b\u3093\u3002<\/li><li>\u30d9\u30af\u30c8\u30eb\u7dda\u307e\u305f\u306f\u76f4\u7dda: \u6b21\u5143 1 \u306e<span><a href=\"https:\/\/science-hub.click\/?p=5244\">\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<\/a><\/span><i>E<\/i>\u3092\u6307\u5b9a\u3057\u307e\u3059\u3002E \u306e\u30bc\u30ed<span><a href=\"https:\/\/science-hub.click\/?p=95765\">\u4ee5\u5916<\/a><\/span>\u306e\u30d9\u30af\u30c8\u30eb\u306f<i>E<\/i>\u306e\u57fa\u5e95\u3092\u5f62\u6210\u3057\u307e\u3059<i>\u3002<\/i><\/li><li>\u30d9\u30af\u30c8\u30eb\u5e73\u9762\u307e\u305f\u306f\u5e73\u9762: \u6b21\u5143<i>2<\/i>\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<i>E<\/i>\u3092\u6307\u5b9a\u3057\u307e\u3059\u3002E \u306e\u975e\u5171\u7dda\u30d9\u30af\u30c8\u30eb\u306e<span><a href=\"https:\/\/science-hub.click\/?p=62815\">\u30da\u30a2<\/a><\/span>( <i>u<\/i> \u3001 <i>v<\/i> ) \u306f<i>E<\/i>\u306e\u57fa\u5e95\u3092\u5f62\u6210\u3057\u307e\u3059\u3002<\/li><\/ul><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/cJ5JM6pnGTI\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u4f8b<\/h2><p>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143\u306f\u3001\u6b63\u898f\u57fa\u5e95\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u3067\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p><ul><li>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u3057\u3066\u898b\u3089\u308c\u308b\u30d5\u30a3\u30fc\u30eb\u30c9<b>K<\/b>\u306f\u3001\u6b21\u5143 1 \u3092\u6301\u3061\u307e\u3059\u3002\u4efb\u610f\u306e<span><a href=\"https:\/\/science-hub.click\/?p=62281\">\u81ea\u7136\u6570<\/a><\/span><i>n<\/i> &gt; 0 \u306e\u5834\u5408\u3001<span><a href=\"https:\/\/science-hub.click\/?p=33222\">\u30c7\u30ab\u30eb\u30c8\u7a4d<\/a><\/span><b>K<\/b> <sup><i>n \u306f\u3001<\/i><\/sup><span><a href=\"https:\/\/science-hub.click\/?p=39965\">\u30b9\u30ab\u30e9\u30fc<\/a><\/span>\u306e<i>n<\/i>\u30bf\u30d7\u30eb\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3059\u3002\u3053\u308c\u306f\u6b21\u5143<i>n<\/i>\u3067\u3042\u308a\u3001\u305d\u306e<span><a href=\"https:\/\/science-hub.click\/?p=1790\">\u6b63\u6e96\u57fa\u5e95\u306f<\/a><\/span>\u6b63\u78ba\u306b<i>n \u500b\u306e<\/i>\u30d9\u30af\u30c8\u30eb\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u5b9a\u7fa9\u304b\u3089\u3001 <b>K<\/b> <sup><i>n<\/i><\/sup>\u306e\u3059\u3079\u3066\u306e\u57fa\u5e95\u306b\u306f\u6b63\u78ba\u306b<i>n \u500b\u306e<\/i>\u30d9\u30af\u30c8\u30eb\u304c\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002<\/li><li>\u3088\u308a\u4e00\u822c\u7684\u306b\u306f\u3001\u4efb\u610f\u306e<span><a href=\"https:\/\/science-hub.click\/?p=57227\">\u96c6\u5408<\/a><\/span><i>A<\/i>\u306b\u3064\u3044\u3066\u3001\u5bb6\u65cf\u306e\u96c6\u5408\u3092<b>K<\/b> <sup>( <i>A<\/i> )<\/sup>\u3068\u8868\u3057\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {(\\lambda_a)_{a\\in A}} $$<\/div> <i>A<\/i>\u306b\u3088\u3063\u3066\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u4ed8\u3051\u3055\u308c\u3001\u6709\u9650\u306e\u30b5\u30dd\u30fc\u30c8\u3092\u6301\u3064<b>K<\/b>\u306e\u8981\u7d20\u3002\u9805\u3054\u3068\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u30b9\u30ab\u30e9\u30fc\u306b\u3088\u308b<span><a href=\"https:\/\/science-hub.click\/?p=30030\">\u52a0\u7b97<\/a><\/span>\u3068<span><a href=\"https:\/\/science-hub.click\/?p=57404\">\u4e57\u7b97<\/a><\/span>\u3001 <b>K<\/b> <sup>( <i>A<\/i> )<\/sup>\u306f<b>K<\/b>\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3059\u3002\u305d\u306e\u6b63\u7d71\u306a\u57fa\u76e4\u306f\u5bb6\u65cf\u3067\u3059<div class=\"math-formual notranslate\">$$ {(e_a)_{a\\in A}} $$<\/div> \u3001 \u307e\u305f\u306f<div class=\"math-formual notranslate\">$$ {e_b=\\left(\\delta_{ab}\\right)_{a\\in A}} $$<\/div>\u306e\u305f\u3081\u306b<div class=\"math-formual notranslate\">$$ {b\\in A} $$<\/div> \u3002\u3057\u305f\u304c\u3063\u3066\u3001 <b>K<\/b> <sup>( <i>A<\/i> )<\/sup>\u306e\u6b21\u5143\u306f<i>A<\/i>\u306e\u57fa\u6570\u306b\u306a\u308a\u307e\u3059\u3002<\/li><li>\u30d5\u30a3\u30fc\u30eb\u30c9\u5185\u306e\u4fc2\u6570\u3092\u542b\u3080\u591a\u9805\u5f0f<div class=\"math-formual notranslate\">$$ {\\mathbb{K}} $$<\/div> <span><i>n<\/i><\/span>\u4ee5\u4e0b\u306e\u6b21\u6570\u306f\u3001\u6b21\u5143\u304c<span><i>n<\/i> + 1<\/span>\u3067\u3042\u308b<b>K<\/b> [X] \u306e<span><a href=\"https:\/\/science-hub.click\/?p=83297\">\u30d9\u30af\u30c8\u30eb\u90e8\u5206\u7a7a\u9593<\/a><\/span><i>E \u3092<\/i>\u5f62\u6210\u3057\u307e\u3059\u3002\u5bb6\u65cf<div class=\"math-formual notranslate\">$$ {(1,X,\\dots,X^n)} $$<\/div>\u306f<i>E<\/i>\u306e\u6b63\u898f\u306e\u57fa\u790e\u3067\u3059\u3002<\/li><li>\u30d5\u30a3\u30fc\u30eb\u30c9\u5185\u306e\u4fc2\u6570\u3092\u542b\u3080<span><i>n<\/i><\/span>\u884c<span><i>p<\/i><\/span>\u5217\u306e\u884c\u5217\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<div class=\"math-formual notranslate\">$$ {\\mathbb{K}} $$<\/div> \u3001\u6b21\u5143\u304c\u3042\u308b<div class=\"math-formual notranslate\">$$ {n\\cdot p} $$<\/div> \u3002 <span><i>i<\/i><\/span>\u756a\u76ee\u306e\u884c\u3068<span><i>j<\/i><\/span>\u756a\u76ee\u306e\u5217\u306b 1 \u304c\u3042\u308a\u3001\u305d\u306e\u4ed6\u306e\u5834\u6240\u306b 0 \u304c\u3042\u308b\u884c\u5217\u3067\u69cb\u6210\u3055\u308c\u308b\u30d5\u30a1\u30df\u30ea\u30fc<span>( <i>E<\/i> <sub><i>i<\/i> <i>j<\/i><\/sub> )<\/span>\u304c\u3001\u3053\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u57fa\u790e\u3067\u3059\u3002<\/li><\/ul><p>\u30b9\u30ab\u30e9\u30fc\u672c\u4f53\u306e\u9078\u629e\u306f\u91cd\u8981\u3067\u3059\u3002<\/p><ul><li>\u8907\u7d20\u6570\u306e\u30bb\u30c3\u30c8\u306f\u3001 <div class=\"math-formual notranslate\">$$ {\\mathbf R} $$<\/div> -\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u540c\u69d8\u306b<div class=\"math-formual notranslate\">$$ {\\mathbf C} $$<\/div> -\u30d9\u30af\u30c8\u30eb\u7a7a\u9593;\u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059<div class=\"math-formual notranslate\">$$ {{\\rm dim}_{\\mathbf{R}}(\\mathbf{C})=2} $$<\/div>\u305d\u3057\u3066<div class=\"math-formual notranslate\">$$ {{\\rm dim}_{\\mathbf{C}}(\\mathbf{C})=1} $$<\/div> \u3002<\/li><\/ul><h2>\u4e00\u822c\u5316<\/h2><p>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092<span><a href=\"https:\/\/science-hub.click\/?p=33034\">matroid<\/a><\/span>\u306e\u7279\u6b8a\u306a\u30b1\u30fc\u30b9\u3068\u3057\u3066\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u5f8c\u8005\u306b\u306f\u660e\u78ba\u306b\u5b9a\u7fa9\u3055\u308c\u305f\u6b21\u5143\u306e\u6982\u5ff5\u304c\u3042\u308a\u307e\u3059\u3002\u30e2\u30b8\u30e5\u30fc\u30eb\u306e<span><a href=\"https:\/\/science-hub.click\/?p=17420\">\u9577\u3055<\/a><\/span>\u3068\u30a2\u30fc\u30d9\u30eb\u7fa4\u306e<span><a href=\"https:\/\/science-hub.click\/?p=23588\">\u30e9\u30f3\u30af<\/a><\/span>\u306e\u4e21\u65b9\u306b\u306f\u3001\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143\u306b\u4f3c\u305f\u3044\u304f\u3064\u304b\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/LinKnW2VVhI\/0.jpg\" style=\"width:100%;\"\/><\/figure><h2>\u30d7\u30ed\u30d1\u30c6\u30a3<\/h2><p><span><i>F<\/i><\/span>\u304c<span><i>E<\/i><\/span>\u306e\u30d9\u30af\u30c8\u30eb\u90e8\u5206\u7a7a\u9593\u306e\u5834\u5408\u3001 <div class=\"math-formual notranslate\">$$ {{\\rm dim}(F)\\leq {\\rm dim}(E)} $$<\/div> \u3002<\/p><p> 2 \u3064\u306e\u6709\u9650\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u304c\u7b49\u3057\u3044\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u306b\u3001\u6b21\u306e\u5b9a\u7406\u304c\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 <span><i>E<\/i><\/span>\u304c\u6709\u9650\u6b21\u5143\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3001 <span><i>F \u304c<\/i><\/span><span><i>E<\/i><\/span>\u306e\u30d9\u30af\u30c8\u30eb\u90e8\u5206\u7a7a\u9593\u3067\u3042\u308a\u3001 <span>dim <i>F<\/i> = dim <i>E<\/i><\/span>\u3067\u3042\u308b\u5834\u5408\u3001 <span><i>E<\/i> = <i>F<\/i><\/span>\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u542b\u610f\u306f\u7121\u9650\u6b21\u5143\u3067\u306f\u507d\u306b\u306a\u308a\u307e\u3059\u3002\u7dda\u5f62\u30de\u30c3\u30d7\u306b\u95a2\u3059\u308b\u6b21\u5143\u306b\u95a2\u3059\u308b\u91cd\u8981\u306a\u7d50\u679c\u306f\u3001\u30e9\u30f3\u30af\u5b9a\u7406\u3067\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/6lKtkf3SNyE\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u5206\u985e<\/span><\/h3><p>\u4e0a\u306e 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<div class=\"math-formual notranslate\">$$ {\\mathbb{K}} $$<\/div>\u305d\u308c\u3089\u304c\u540c\u3058\u6b21\u5143\u3092\u6301\u3064\u5834\u5408\u306b\u306e\u307f\u3001\u6709\u9650\u6b21\u5143\u3067\u540c\u578b\u3068\u306a\u308a\u307e\u3059\u3002<\/p><p>\u305d\u308c\u3089\u306e\u57fa\u5e95\u9593\u306e\u5168\u5358\u5c04\u30de\u30c3\u30d7\u306f\u30012 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u9593\u306e\u540c\u578b\u5199\u50cf\u306b\u4e00\u610f\u306b\u62e1\u5f35\u3067\u304d\u307e\u3059\u3002 <span><i>A<\/i><\/span>\u304c\u96c6\u5408\u306e\u5834\u5408\u3001\u6b21\u5143<span>|<\/span>\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<span><i>\u3042<\/i>|<\/span>\u306e\u4e0a<div class=\"math-formual notranslate\">$$ {\\mathbb{K}} $$<\/div>\u306f\u6b21\u306e\u65b9\u6cd5\u3067\u69cb\u7bc9\u3067\u304d\u307e\u3059: \u30bb\u30c3\u30c8\u3092\u8003\u616e\u3057\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\mathbb{K}^{(A)}} $$<\/div>\u3059\u3079\u3066\u306e\u6a5f\u80fd\u306e<div class=\"math-formual notranslate\">$$ {f:A\\rightarrow \\mathbb{K}} $$<\/div> <span><i>A<\/i><\/span>\u306e\u6709\u9650\u6570\u306e\u8981\u7d20<span><i>a<\/i><\/span>\u306b\u5bfe\u3057\u3066<span><i>f<\/i> ( <i>a<\/i> ) = 0<\/span>\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u95a2\u6570\u306f\u3001\u6b21\u306e\u30b9\u30ab\u30e9\u30fc\u3067\u52a0\u7b97\u304a\u3088\u3073\u4e57\u7b97\u3067\u304d\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {\\mathbb{K}} $$<\/div> \u3001\u305d\u3057\u3066\u3001\u79c1\u305f\u3061\u306f\u5f97\u307e\u3059<div class=\"math-formual notranslate\">$$ {\\mathbb{K}} $$<\/div> -\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092\u7814\u7a76\u3057\u307e\u3057\u305f\u3002<\/p><h3> <span>K\u306e\u4fee\u6b63<\/span><\/h3><p><span><i>L<\/i> \/ <i>K \u3092<\/i><\/span><span><a href=\"https:\/\/science-hub.click\/?p=36452\">\u30dc\u30c7\u30a3\u30a8\u30af\u30b9\u30c6\u30f3\u30b7\u30e7\u30f3<\/a><\/span>\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001 <span><i>L \u306f<\/i><\/span><span><i>K<\/i><\/span>\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3042\u308a\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5408\u8a08\u306f\u4f53 L \u5185\u306e\u5408\u8a08\u3067\u3042\u308a\u3001\u30b9\u30ab\u30e9\u30fc\u306b\u3088\u308b\u4e57\u7b97\u304c\u5236\u9650\u3068\u306a\u308a\u307e\u3059\u3002 <div class=\"math-formual notranslate\">$$ {K\\times L} $$<\/div> K \u4e0a\u306e L \u306e\u6b21\u5143\u306f\u62e1\u5f35<b>\u6307\u6570<\/b>\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3053\u306e\u5b9a\u7fa9\u306f\u3001<i>\u672c\u6587\u62e1\u5f35<\/i>\u306e\u8a18\u4e8b\u3067\u53d6\u308a\u4e0a\u3052\u3089\u308c\u3001\u30b3\u30e1\u30f3\u30c8\u3055\u308c\u3066\u3044\u307e\u3059\u3002<\/p><p>\u3055\u3089\u306b\u3001\u4e57\u7b97\u306e\u5236\u9650\u306b\u3088\u308a\u3001\u3059\u3079\u3066\u306e<span><i>L<\/i><\/span>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<span><i>E \u306f<\/i><\/span><span><i>K<\/i><\/span>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3082\u3042\u308a\u307e\u3059\u3002\u5bf8\u6cd5\u306f\u6b21\u306e\u5f0f\u3067\u95a2\u9023\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002 <\/p><dl><dd><div class=\"math-formual notranslate\">$$ {{\\rm dim}_K(E)={\\rm dim}_K(L)\\cdot {\\rm dim}_L(E)} $$<\/div> \u3002<\/dd><\/dl><p>\u7279\u306b\u3001\u6b21\u5143<span><i>n<\/i><\/span>\u306e\u8907\u7d20\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306f\u6b21\u5143<span>2 <i>n<\/i><\/span>\u306e\u5b9f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3059\u3002<\/p><figure class=\"wp-block-image size-large is-style-default\">\n<img decoding=\"async\" alt=\"\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143 - \u5b9a\u7fa9\" class=\"aligncenter\" onerror=\"this.style.display=none;\" src=\"https:\/\/img.youtube.com\/vi\/mYJDns0vihI\/0.jpg\" style=\"width:100%;\"\/><\/figure><h3><span>\u30c7\u30a3\u30e1\u30f3\u30b7\u30e7\u30f3\u3068\u30ab\u30fc\u30c7\u30a3\u30ca\u30eb<\/span><\/h3><p>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<b>K<\/b> <sup>( <i>A<\/i> )<\/sup>\u306e\u6b21\u5143\u306f<i>A<\/i>\u306e\u57fa\u6570\u3067\u3059\u3002\u3053\u306e\u4e3b\u5f35\u304b\u3089\u3001\u30b9\u30ab\u30e9\u30fc\u5834<b>K<\/b>\u306e\u57fa\u6570\u3001\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<i>E<\/i>\u306e\u57fa\u6570\u3001\u304a\u3088\u3073<b>K<\/b>\u4e0a\u306e\u305d\u306e\u6b21\u5143\u3092\u7d50\u3073\u4ed8\u3051\u308b\u6b21\u306e\u95a2\u4fc2\u304c\u5c0e\u304d\u51fa\u3055\u308c\u307e\u3059\u3002<\/p><ul><li> <span>dim <sub><i>K<\/i><\/sub> <i>E<\/i><\/span>\u304c\u6709\u9650\u306e\u5834\u5408\u3001 <span>| <i>E<\/i> | = | <i>K<\/i> |<sup>\u30b5\u30f3<i>E.<\/i><\/sup><\/span><\/li><li> <span>dim <sub><i>K<\/i><\/sub> <i>E<\/i><\/span>\u304c\u7121\u9650\u5927\u306e\u5834\u5408\u3001 <span>| <i>E<\/i> | = max(dim <i>E<\/i> , | <i>K<\/i> | )<\/span> \u3002<\/li><\/ul><p>\u7279\u306b\u3001 <b>K<\/b>\u304c\u6709\u9650\u3067<i>E<\/i>\u304c\u6709\u9650\u6b21\u5143\u3067\u3042\u308b\u5834\u5408\u3001 <b>K<\/b>\u30d9\u30af\u30c8\u30eb\u7a7a\u9593<i>E \u306f<\/i>\u6709\u9650\u3067\u3059\u3002<\/p><p>\u7279\u306b\u3001<span><a href=\"https:\/\/science-hub.click\/?p=66269\">\u6709\u9650\u4f53<\/a><\/span><b>L \u306f\u3001<\/b>\u305d\u306e\u7d20\u4f53<b>K<\/b>\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u3057\u3066\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u7d20\u4f53 K \u306f\u3001\u57fa\u6570\u304c<span><a href=\"https:\/\/science-hub.click\/?p=16478\">\u7d20\u6570<\/a><\/span><i>p<\/i>\u3067\u3042\u308a\u3001 <b>L<\/b>\u306e\u7279\u6027\u3068\u547c\u3070\u308c\u307e\u3059\u3002 <i>n \u304c<\/i><b>K<\/b>\u4e0a\u306e<b>L<\/b>\u306e\u6b21\u5143\u3067\u3042\u308b\u5834\u5408\u3001 <b>L \u306f<\/b>\u57fa\u6570<i>p<\/i> <sup><i>n<\/i><\/sup>\u306e\u3082\u306e\u306b\u306a\u308a\u307e\u3059\u3002\u6709\u9650\u4f53\u306e\u57fa\u6570\u306f\u3001\u305d\u306e\u7279\u6027\u306e\u6574\u6570<span><a href=\"https:\/\/science-hub.click\/?p=15958\">\u4e57<\/a><\/span>\u3067\u3059\u3002<\/p><\/div><h2 class=\"ref_link\">\u53c2\u8003\u8cc7\u6599<\/h2><ol><li><a class=\"notranslate\" href=\"https:\/\/ar.wikipedia.org\/wiki\/%D8%A8%D8%B9%D8%AF_(%D9%81%D8%B6%D8%A7%D8%A1_%D9%85%D8%AA%D8%AC%D9%87%D9%8A)\">\u0628\u0639\u062f (\u0641\u0636\u0627\u0621 \u0645\u062a\u062c\u0647\u064a) \u2013 arabe<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/ca.wikipedia.org\/wiki\/Dimensi%C3%B3_d%27un_espai_vectorial\">Dimensi\u00f3 d&#8217;un espai vectorial \u2013 catalan<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/cs.wikipedia.org\/wiki\/Dimenze_vektorov%C3%A9ho_prostoru\">Dimenze vektorov\u00e9ho prostoru \u2013 tch\u00e8que<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/de.wikipedia.org\/wiki\/Hamel-Dimension\">Hamel-Dimension \u2013 allemand<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/en.wikipedia.org\/wiki\/Dimension_(vector_space)\">Dimension (vector space) \u2013 anglais<\/a><\/li><li> <a class=\"notranslate\" href=\"https:\/\/es.wikipedia.org\/wiki\/Dimensi%C3%B3n_de_un_espacio_vectorial\">Dimensi\u00f3n de un espacio vectorial \u2013 espagnol<\/a><\/li><\/ol><\/div>\n<div class=\"feature-video\">\n <h2>\n  \u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143 &#8211; \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n <div class=\"video-item\">\n  \n  <figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\n   <div class=\"wp-block-embed__wrapper\">\n    <iframe loading=\"lazy\" title=\"\u3010\u5927\u5b66\u6570\u5b66\u3011\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u2460(\u5b9a\u7fa9)\/\u51683\u56de\u3010\u7dda\u5f62\u4ee3\u6570\u3011\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/F0mkAiRiLik?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n   <\/div>\n  <\/figure>\n  \n <\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u5c0e\u5165 \u7dda\u5f62\u4ee3\u6570\u3067\u306f\u3001\u30cf\u30e1\u30eb\u6b21\u5143\u3001\u307e\u305f\u306f\u5358\u306b\u6b21\u5143\u306f\u3001\u7269\u4f53K\u4e0a\u306e\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u7a7a\u9593E\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u305f\u4e0d\u5909\u91cf\u3067\u3059\u3002 E\u306e\u6b21\u5143\u306f\u3001\u305d\u306e\u3059\u3079\u3066\u306e\u57fa\u5e95\u306b\u5171\u901a\u306e\u57fa\u6570\u3067\u3059\u3002\u3053\u306e\u6570\u306fdim K ( E ) (\u300c K\u4e0a\u306eE\u306e\u6b21\u5143\u300d\u3068\u8aad\u307f\u307e\u3059 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":101628,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/img.youtube.com\/vi\/F0mkAiRiLik\/0.jpg","fifu_image_alt":"\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u6b21\u5143 - \u5b9a\u7fa9","footnotes":""},"categories":[5],"tags":[88697,11,13,14,10,6337,12,12224,8,16,293,15,9],"class_list":["post-101627","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dictionary","tag-arvicola","tag-techniques","tag-technologie","tag-news","tag-actualite","tag-vectoriel","tag-dossier","tag-dimension","tag-definition","tag-sciences","tag-espace","tag-article","tag-explications"],"_links":{"self":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/101627"}],"collection":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=101627"}],"version-history":[{"count":0,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/posts\/101627\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=\/wp\/v2\/media\/101628"}],"wp:attachment":[{"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=101627"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=101627"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/science-hub.click\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=101627"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}