[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2019\/09\/30\/%e6%a5%b5%e5%8c%96%e6%81%92%e7%ad%89%e5%bc%8f-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2019\/09\/30\/%e6%a5%b5%e5%8c%96%e6%81%92%e7%ad%89%e5%bc%8f-wikipedia\/","headline":"\u6975\u5316\u6052\u7b49\u5f0f – Wikipedia","name":"\u6975\u5316\u6052\u7b49\u5f0f – Wikipedia","description":"\u6975\u5316\u6052\u7b49\u5f0f\u3092\u793a\u3059\u30d9\u30af\u30c8\u30eb \u6570\u5b66\u306b\u304a\u3044\u3066\u3001 \u6975\u5316\u6052\u7b49\u5f0f\uff08\u304d\u3087\u304f\u304b\u3053\u3046\u3068\u3046\u3057\u304d\uff09\u3042\u308b\u3044\u306f\u504f\u6975\u6052\u7b49\u5f0f\uff08\u3078\u3093\u304d\u3087\u304f\u3053\u3046\u3068\u3046\u3057\u304d\uff09\uff08\u82f1\uff1apolarization identity\uff09\u3068\u306f\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u30ce\u30eb\u30e0\u7dda\u578b\u7a7a\u9593\u306e\u30ce\u30eb\u30e0\u3067\u8868\u73fe\u3059\u308b\u6052\u7b49\u5f0f\u3067\u3042\u308b\u3002 \u2016x\u2016{displaystyle |x|} \u3092\u30d9\u30af\u30c8\u30eb x \u306e\u30ce\u30eb\u30e0\u3001 \u27e8x,\u00a0y\u27e9{displaystyle langle x, yrangle } \u3092\u30d9\u30af\u30c8\u30eb x \u3068 y \u306e\u5185\u7a4d\u3068\u3059\u308b\u3068\u3001\u30d5\u30ec\u30b7\u30a7\u3001\u30ce\u30a4\u30de\u30f3\u3001\u30e8\u30eb\u30c0\u30f3\u306b\u3088\u308b\u57fa\u672c\u7684\u5b9a\u7406\u306f\u6b21\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3055\u308c\u308b [1][2]\u3002","datePublished":"2019-09-30","dateModified":"2019-09-30","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki4\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d5\/Parallelogram_law.svg\/220px-Parallelogram_law.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/d\/d5\/Parallelogram_law.svg\/220px-Parallelogram_law.svg.png","height":"267","width":"220"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2019\/09\/30\/%e6%a5%b5%e5%8c%96%e6%81%92%e7%ad%89%e5%bc%8f-wikipedia\/","wordCount":20083,"articleBody":"  \u6975\u5316\u6052\u7b49\u5f0f\u3092\u793a\u3059\u30d9\u30af\u30c8\u30eb\u6570\u5b66\u306b\u304a\u3044\u3066\u3001 \u6975\u5316\u6052\u7b49\u5f0f\uff08\u304d\u3087\u304f\u304b\u3053\u3046\u3068\u3046\u3057\u304d\uff09\u3042\u308b\u3044\u306f\u504f\u6975\u6052\u7b49\u5f0f\uff08\u3078\u3093\u304d\u3087\u304f\u3053\u3046\u3068\u3046\u3057\u304d\uff09\uff08\u82f1\uff1apolarization identity\uff09\u3068\u306f\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5185\u7a4d\u3092\u30ce\u30eb\u30e0\u7dda\u578b\u7a7a\u9593\u306e\u30ce\u30eb\u30e0\u3067\u8868\u73fe\u3059\u308b\u6052\u7b49\u5f0f\u3067\u3042\u308b\u3002 \u2016x\u2016{displaystyle |x|} \u3092\u30d9\u30af\u30c8\u30eb x \u306e\u30ce\u30eb\u30e0\u3001\u27e8x,\u00a0y\u27e9{displaystyle langle x, yrangle } \u3092\u30d9\u30af\u30c8\u30eb x \u3068 y \u306e\u5185\u7a4d\u3068\u3059\u308b\u3068\u3001\u30d5\u30ec\u30b7\u30a7\u3001\u30ce\u30a4\u30de\u30f3\u3001\u30e8\u30eb\u30c0\u30f3\u306b\u3088\u308b\u57fa\u672c\u7684\u5b9a\u7406\u306f\u6b21\u306e\u3088\u3046\u306b\u8a18\u8ff0\u3055\u308c\u308b [1][2]\u3002\u30ce\u30eb\u30e0\u7a7a\u9593 (V, \u2016\u22c5\u2016{displaystyle |cdot |}) \u306b\u304a\u3044\u3066\u3001\u4e2d\u7dda\u5b9a\u7406\u304c\u6210\u308a\u7acb\u3064\u306a\u3089\u3070\u3001V  \u306b\u306f\u3059\u3079\u3066\u306e x\u2208V{displaystyle xin V} \u3067 \u2016x\u20162=\u27e8x,\u00a0x\u27e9{displaystyle |x|^{2}=langle x, xrangle } \u3092\u6e80\u305f\u3059\u5185\u7a4d\u304c\u5b58\u5728\u3059\u308b\u3002\u4ee5\u4e0b\u306b\u793a\u3059\u69d8\u3005\u306a\u5f62\u306e\u6975\u5316\u6052\u7b49\u5f0f\u306f\u3059\u3079\u3066\u3001\u3053\u306e\u4e2d\u7dda\u5b9a\u7406\u306b\u95a2\u9023\u3059\u308b\u3082\u306e\u3067\u3042\u308b\u30022\u2016u\u20162+2\u2016v\u20162=\u2016u+v\u20162+\u2016u\u2212v\u20162.{displaystyle 2|{textbf {u}}|^{2}+2|{textbf {v}}|^{2}=|{textbf {u}}+{textbf {v}}|^{2}+|{textbf {u}}-{textbf {v}}|^{2}.}\u6975\u5316\u6052\u7b49\u5f0f\u306f\u3001\u62bd\u8c61\u4ee3\u6570\u5b66\u3084\u7dda\u5f62\u4ee3\u6570\u5b66\u3001\u95a2\u6570\u89e3\u6790\u5b66\u3068\u3044\u3063\u305f\u69d8\u3005\u306a\u5206\u91ce\u306e\u8868\u73fe\u306b\u4e00\u822c\u5316\u3067\u304d\u308b\u3002Table of Contents\u5b9f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u5834\u5408[\u7de8\u96c6]\u8907\u7d20\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u5834\u5408[\u7de8\u96c6]\u5b9f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u4ed6\u306e\u8868\u73fe[\u7de8\u96c6]\u8a3c\u660e[\u7de8\u96c6]\u30c9\u30c3\u30c8\u7a4d\u3078\u306e\u5fdc\u7528[\u7de8\u96c6]\u4f59\u5f26\u5b9a\u7406\u3068\u306e\u95a2\u4fc2[\u7de8\u96c6]\u5c0e\u51fa[\u7de8\u96c6]\u30ce\u30eb\u30e0[\u7de8\u96c6]\u5bfe\u79f0\u53cc\u7dda\u5f62\u5f62\u5f0f[\u7de8\u96c6]\u8907\u7d20\u6570[\u7de8\u96c6]\u9ad8\u6b21\u306e\u6589\u6b21\u591a\u9805\u5f0f[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u5b9f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u5834\u5408[\u7de8\u96c6]V \u304c\u5b9f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u5834\u5408\u3001\u5185\u7a4d\u306f\u4ee5\u4e0b\u306e\u6975\u5316\u6052\u7b49\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u3002\u27e8x,\u00a0y\u27e9=14(\u2016x+y\u20162\u2212\u2016x\u2212y\u20162)\u00a0\u2200\u00a0x,y\u2208V{displaystyle langle x, yrangle ={frac {1}{4}}left(|x+y|^{2}-|x-y|^{2}right) forall  x,yin V}  \u8907\u7d20\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u5834\u5408[\u7de8\u96c6]V \u304c\u8907\u7d20\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u5834\u5408\u3001\u5185\u7a4d\u306f\u4ee5\u4e0b\u306e\u6975\u5316\u6052\u7b49\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u3002\u27e8x,\u00a0y\u27e9=14(\u2016x+y\u20162\u2212\u2016x\u2212y\u20162+i\u2016x\u2212iy\u20162\u2212i\u2016x+iy\u20162)\u00a0\u2200\u00a0x,y\u2208V{displaystyle langle x, yrangle ={frac {1}{4}}left(|x+y|^{2}-|x-y|^{2}+i|x-iy|^{2}-i|x+iy|^{2}right) forall  x,yin V}\u3053\u3053\u3067   i{displaystyle i} \u306f\u865a\u6570\u5358\u4f4d\u3067\u3042\u308b\u3002 \u3053\u306e\u5f0f\u306f\u3001\u7b2c\u4e00\u5909\u6570\u304c\u53cd\u7dda\u5f62\u3067\u3001\u7b2c\u4e8c\u5909\u6570\u304c\u7dda\u5f62\u3067\u3042\u308b\u5185\u7a4d\u3092\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u305b\u3088\u3002 \u9006\u306e\u5b9a\u7fa9\u3092\u4f7f\u7528\u3059\u308b\u898f\u5247\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8907\u7d20\u5171\u5f79\u3092\u53d6\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u27e8x,\u00a0y\u27e9=14(\u2016x+y\u20162\u2212\u2016x\u2212y\u20162\u2212i\u2016x\u2212iy\u20162+i\u2016x+iy\u20162)\u00a0\u2200\u00a0x,y\u2208V{displaystyle langle x, yrangle ={frac {1}{4}}left(|x+y|^{2}-|x-y|^{2}-i|x-iy|^{2}+i|x+iy|^{2}right) forall  x,yin V}\u5b9f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u306e\u4ed6\u306e\u8868\u73fe[\u7de8\u96c6]\u4e2d\u7dda\u5b9a\u7406\u3092\u4f7f\u7528\u3057\u3066\u3001\u4ed6\u306e\u8868\u73fe\u3092\u5c0e\u51fa\u3067\u304d\u308b\u3002  u\u22c5v=12(\u2016u+v\u20162\u2212\u2016u\u20162\u2212\u2016v\u20162)(1)u\u22c5v=12(\u2016u\u20162+\u2016v\u20162\u2212\u2016u\u2212v\u20162)(2)u\u22c5v=14(\u2016u+v\u20162\u2212\u2016u\u2212v\u20162)(3){displaystyle {begin{aligned}{textbf {u}}cdot {textbf {v}}&={frac {1}{2}}left(|{textbf {u}}+{textbf {v}}|^{2}-|{textbf {u}}|^{2}-|{textbf {v}}|^{2}right)&(1)[0.5em]{textbf {u}}cdot {textbf {v}}&={frac {1}{2}}left(|{textbf {u}}|^{2}+|{textbf {v}}|^{2}-|{textbf {u}}-{textbf {v}}|^{2}right)&(2)[0.5em]{textbf {u}}cdot {textbf {v}}&={frac {1}{4}}left(|{textbf {u}}+{textbf {v}}|^{2}-|{textbf {u}}-{textbf {v}}|^{2}right)&(3)end{aligned}}}\u30ce\u30eb\u30e0\u7a7a\u9593 (V , \u2016\u22c5\u2016{displaystyle |cdot |}) \u306b\u304a\u3044\u3066\u3001 \u4e2d\u7dda\u5b9a\u7406\u304c\u6210\u308a\u7acb\u3064\u306a\u3089\u3070\u3001 V  \u306b\u306f\u3059\u3079\u3066\u306e x\u2208V{displaystyle xin V} \u3067 \u2016x\u20162=\u27e8x,\u00a0x\u27e9{displaystyle |x|^{2}=langle x, xrangle } \u3092\u6e80\u305f\u3059\u5185\u7a4d\u304c\u5b58\u5728\u3059\u308b\u3002\u8a3c\u660e[\u7de8\u96c6]\u5b9f\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3092\u8003\u3048\u308b\u3002\u3059\u308b\u3068\u3001\u6975\u5316\u6052\u7b49\u5f0f\u304b\u3089\u300c\u5185\u7a4d\u300d\uff08\u3068\u601d\u308f\u308c\u308b\u3082\u306e\uff09\u304c\u5f97\u3089\u308c\u308b\u3002\u27e8x,\u00a0y\u27e9=14(\u2016x+y\u20162\u2212\u2016x\u2212y\u20162)\u00a0\u2200\u00a0x,y\u2208V{displaystyle langle x, yrangle ={frac {1}{4}}left(|x+y|^{2}-|x-y|^{2}right) forall  x,yin V}\u305d\u3053\u3067\u3001\u3053\u306e\u300c\u5185\u7a4d\u300d\u304c\u5b9f\u969b\u306b\u5185\u7a4d\u306e\u6027\u8cea\u3092\u6e80\u305f\u3057\u3001\u3053\u306e\u5185\u7a4d\u304b\u3089\u5c0e\u304b\u308c\u308b\u30ce\u30eb\u30e0\u304c (V ,  \u2016\u22c5\u2016{displaystyle |cdot |}) \u3092\u5b9a\u7fa9\u3059\u308b\u30ce\u30eb\u30e0 \u2016\u22c5\u2016{displaystyle |cdot |} \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u3002\u27e8\u22c5,\u22c5\u27e9{displaystyle langle cdot ,cdot rangle } \u304c\u5185\u7a4d\u3067\u3042\u308b\u305f\u3081\u306b\u306f\u3001\u6b21\u306e\u6027\u8cea\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308b\u3002"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki4\/2019\/09\/30\/%e6%a5%b5%e5%8c%96%e6%81%92%e7%ad%89%e5%bc%8f-wikipedia\/#breadcrumbitem","name":"\u6975\u5316\u6052\u7b49\u5f0f – Wikipedia"}}]}]