[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/119185#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/119185","headline":"\u4e8c\u6b21\u66f2\u9762 – Wikipedia","name":"\u4e8c\u6b21\u66f2\u9762 – Wikipedia","description":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u4e8c\u6b21\u66f2\u9762”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082015\u5e7410\u6708\uff09 \u4e8c\u6b21\u8d85\u66f2\u9762\uff08\u306b\u3058\u3061\u3087\u3046\u304d\u3087\u304f\u3081\u3093\u3001\u82f1: quadric surface\uff09\u3068\u306f\u3001\u5186\u9310\u66f2\u7dda\u306e\u6982\u5ff5\u3092\u4e00\u822c\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 Rn \u306b\u62e1\u5f35\u3057\u305f\u3082\u306e\u3067\u3042\u308a\u30012\u6b21\u591a\u9805\u5f0f\u306e\u96f6\u70b9\u96c6\u5408\u3068\u3057\u3066\u8868\u3055\u308c\u308b\u3088\u3046\u306a\u8d85\u66f2\u9762\u306e\u3053\u3068\u3092\u3055\u3059\u30023\u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u4e8c\u6b21\u8d85\u66f2\u9762\u306f\u4e8c\u6b21\u66f2\u9762\u3068\u3082\u3088\u3070\u308c\u308b\u3002 \u4e00\u822c\u306a n \u2212 1-\u6b21\u5143\u4e8c\u6b21\u8d85\u66f2\u9762\u306e\u5b9a\u7fa9\u5f0f\u306f\u3001\u5ea7\u6a19 (x1, x2,","datePublished":"2022-03-19","dateModified":"2022-03-19","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/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\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/6\/64\/Question_book-4.svg\/50px-Question_book-4.svg.png","height":"39","width":"50"},"url":"https:\/\/wiki.edu.vn\/jp\/wiki11\/archives\/119185","about":["Wiki"],"wordCount":6153,"articleBody":"\u3053\u306e\u8a18\u4e8b\u306f\u691c\u8a3c\u53ef\u80fd\u306a\u53c2\u8003\u6587\u732e\u3084\u51fa\u5178\u304c\u5168\u304f\u793a\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3001\u4e0d\u5341\u5206\u3067\u3059\u3002\u51fa\u5178\u3092\u8ffd\u52a0\u3057\u3066\u8a18\u4e8b\u306e\u4fe1\u983c\u6027\u5411\u4e0a\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002\u51fa\u5178\u691c\u7d22?:\u00a0“\u4e8c\u6b21\u66f2\u9762”\u00a0\u2013\u00a0\u30cb\u30e5\u30fc\u30b9\u00a0\u00b7 \u66f8\u7c4d\u00a0\u00b7 \u30b9\u30ab\u30e9\u30fc\u00a0\u00b7 CiNii\u00a0\u00b7 J-STAGE\u00a0\u00b7 NDL\u00a0\u00b7 dlib.jp\u00a0\u00b7 \u30b8\u30e3\u30d1\u30f3\u30b5\u30fc\u30c1\u00a0\u00b7 TWL\uff082015\u5e7410\u6708\uff09\u4e8c\u6b21\u8d85\u66f2\u9762\uff08\u306b\u3058\u3061\u3087\u3046\u304d\u3087\u304f\u3081\u3093\u3001\u82f1: quadric surface\uff09\u3068\u306f\u3001\u5186\u9310\u66f2\u7dda\u306e\u6982\u5ff5\u3092\u4e00\u822c\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 Rn \u306b\u62e1\u5f35\u3057\u305f\u3082\u306e\u3067\u3042\u308a\u30012\u6b21\u591a\u9805\u5f0f\u306e\u96f6\u70b9\u96c6\u5408\u3068\u3057\u3066\u8868\u3055\u308c\u308b\u3088\u3046\u306a\u8d85\u66f2\u9762\u306e\u3053\u3068\u3092\u3055\u3059\u30023\u6b21\u5143\u7a7a\u9593\u306b\u304a\u3051\u308b\u4e8c\u6b21\u8d85\u66f2\u9762\u306f\u4e8c\u6b21\u66f2\u9762\u3068\u3082\u3088\u3070\u308c\u308b\u3002  \u4e00\u822c\u306a n \u2212 1-\u6b21\u5143\u4e8c\u6b21\u8d85\u66f2\u9762\u306e\u5b9a\u7fa9\u5f0f\u306f\u3001\u5ea7\u6a19 (x1, x2, …, xn) \u306b\u5bfe\u3057\u3066(\u2211i=1naixi2+2\u2211ixn),A=(a1a12\u22efa1na12a2\u22efa2n\u22ee\u22ee\u22f1\u22eea1na2n\u22efan),b=(b1b2\u22eebn){displaystyle mathbf {x} ={begin{pmatrix}x_{1}\\x_{2}\\vdots \\x_{n}\\end{pmatrix}},quad A={begin{pmatrix}a_{1}&a_{12}&cdots &a_{1n}\\a_{12}&a_{2}&cdots &a_{2n}\\vdots &vdots &ddots &vdots \\a_{1n}&a_{2n}&cdots &a_{n}end{pmatrix}},quad mathbf {b} ={begin{pmatrix}b_{1}\\b_{2}\\vdots \\b_{n}end{pmatrix}}}\u3092\u8003\u3048\u308b\u3068\u3001\u5b9a\u7fa9\u5f0f\u306e 2 \u6b21\u3068 1 \u6b21\u306e\u6589\u6b21\u90e8\u5206\u306f Rn \u306e\u6a19\u6e96\u5185\u7a4d \u27e8\u2022, \u2022\u27e9 \u3092\u4f7f\u3063\u3066\u27e8Ax,x\u27e9=\u2211i=1naixi2+2\u2211i=\u2211i=1nbixi{displaystyle langle Amathbf {x} ,mathbf {x} rangle =sum _{i=1}^{n}a_{i}x_{i}^{2}+2sum _{i+2\u27e8b,x\u27e9+c=0{displaystyle langle Amathbf {x} ,mathbf {x} rangle +2langle mathbf {b} ,mathbf {x} rangle +c=0}\u3068\u3044\u3046\u5f62\u306b\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u308c\u306f\u3055\u3089\u306bx~=(x1)=(x1x2\u22eexn1),R=(Abtbc)=(a1a12\u22efa1nb1a12a2\u22efa2nb2\u22ee\u22ee\u22f1\u22ee\u22eea1na2n\u22efanbnb1b2\u22efbnc){displaystyle {tilde {mathbf {x} }}={begin{pmatrix}mathbf {x} \\1end{pmatrix}}={begin{pmatrix}x_{1}\\x_{2}\\vdots \\x_{n}\\1end{pmatrix}},quad R={begin{pmatrix}A&mathbf {b} \\{}^{t}mathbf {b} &cend{pmatrix}}={begin{pmatrix}a_{1}&a_{12}&cdots &a_{1n}&b_{1}\\a_{12}&a_{2}&cdots &a_{2n}&b_{2}\\vdots &vdots &ddots &vdots &vdots \\a_{1n}&a_{2n}&cdots &a_{n}&b_{n}\\b_{1}&b_{2}&cdots &b_{n}&cend{pmatrix}}}\u3068\u304a\u304f\u3053\u3068\u306b\u3088\u308a\u3001\u27e8Rx~,x~\u27e9=0{displaystyle langle R{tilde {mathbf {x} }},{tilde {mathbf {x} }}rangle =0}\u306e\u5f62\u306b\u306a\u308b\u3002\u3053\u306e\u3068\u304d\u3001A \u3092\u3053\u306e\u4e8c\u6b21\u66f2\u9762\u306e\u4fc2\u6570\u884c\u5217\u3068\u547c\u3073\u3001R \u3092\u3053\u306e\u4e8c\u6b21\u66f2\u9762\u306e\u62e1\u5927\u4fc2\u6570\u884c\u5217\u3068\u547c\u3076\u30022 \u6b21\u306e\u4fc2\u6570\u306b\u95a2\u3059\u308b\u5236\u7d04\u304b\u3089\u3001A \u304a\u3088\u3073 R \u306f\u96f6\u884c\u5217\u306b\u306f\u306a\u3089\u306a\u3044\u3002n \u2212 1-\u6b21\u5143\u4e8c\u6b21\u8d85\u66f2\u9762\u306f\u3001\u305d\u306e\u62e1\u5927\u4fc2\u6570\u884c\u5217\u306e\u968e\u6570\u304c n + 1 \u306b\u7b49\u3057\u3044\u3068\u304d\u975e\u9000\u5316\u3067\u3042\u308b\u3068\u3044\u3044\u3001\u305d\u3046\u3067\u306a\u3044\u3068\u304d\u9000\u5316\u3057\u3066\u3044\u308b\u3068\u3044\u3046\u3002\u4e8c\u6b21\u8d85\u66f2\u9762\u304c\u975e\u9000\u5316\u3067\u3042\u308b\u3068\u304d\u3001\u4fc2\u6570\u884c\u5217 A \u3068\u62e1\u5927\u4fc2\u6570\u884c\u5217 R \u306e\u968e\u6570\u306e\u95a2\u4fc2\u3092\u7528\u3044\u3066\u3001\u4e8c\u6b21\u8d85\u66f2\u9762\u306f\u6b21\u306e\u3088\u3046\u306b\u5206\u985e\u3055\u308c\u308b\u3002rank R \u2212 rank A = 0: \u9310\u9762rank R \u2212 rank A = 1: \u6709\u5fc3\u4e8c\u6b21\u8d85\u66f2\u9762rank R \u2212 rank A = 2: \u7121\u5fc3\u4e8c\u6b21\u8d85\u66f2\u9762\u307e\u305f\u3001\u9000\u5316\u3057\u305f\u4e8c\u6b21\u8d85\u66f2\u9762\u306f\u7b52\u9762\u306e\u4e00\u7a2e\u3067\u3042\u308b\u3002\u4eca\u3001\u6709\u5fc3\u3068\u7121\u5fc3\u3068\u3044\u3046\u8a00\u8449\u304c\u51fa\u3066\u304d\u305f\u304c\u3001\u3053\u308c\u306f\u70b9\u5bfe\u79f0\u3067\u3042\u308b\u304b\u306a\u3044\u304b\u3092\u6307\u3059\u3002\u4e0a\u306e 3 \u3064\u306f\u3001\u9069\u5f53\u306a\u76f4\u4ea4\u5909\u63db\u3092\u884c\u3046\u3053\u3068\u306b\u3088\u3063\u3066\u3001\u6b21\u306e\u3088\u3046\u306a\u9670\u95a2\u6570\u306b\u5e30\u7740\u3067\u304d\u308b\u3002a1\u2032X12+a2\u2032X22+\u22ef+an\u2032Xn2=0{displaystyle a’_{1}X_{1}^{2}+a’_{2}X_{2}^{2}+cdots +a’_{n}X_{n}^{2}=0}a1\u2032X12+a2\u2032X22+\u22ef+an\u2032Xn2=1{displaystyle a’_{1}X_{1}^{2}+a’_{2}X_{2}^{2}+cdots +a’_{n}X_{n}^{2}=1}a1\u2032X12+a2\u2032X22+\u22ef+an\u22121\u2032Xn\u221212+2bXn=1{displaystyle a’_{1}X_{1}^{2}+a’_{2}X_{2}^{2}+cdots +a’_{n-1}X_{n-1}^{2}+2bX_{n}=1}\u4e0a\u306e 3 \u5f0f\u3092\u3001\u975e\u9000\u5316\u306a\u4e8c\u6b21\u8d85\u66f2\u9762\u306e\u6a19\u6e96\u5f62\u3068\u3044\u3046\u3002\u3053\u306e\u6642\u3001\u4e0a\u306e\u4fc2\u6570\u3092\u5bfe\u89d2\u6210\u5206\u306b\u3082\u3064\u884c\u5217\u306f\u9069\u5f53\u306a\u76f8\u4f3c\u5909\u63db\u3092\u884c\u3046\u3053\u3068\u306b\u3088\u308a\u3001\u6b21\u306e\u3088\u3046\u306a\u884c\u5217\u306b\u5909\u63db\u3067\u304d\u308b\u3002S=(Ep000\u2212Eq000(0)){displaystyle S={begin{pmatrix}E_{p}&0&0\\0&-E_{q}&0\\0&0&(0)end{pmatrix}}}\u305f\u3060\u3057\u3001\u53f3\u4e0b\u306e\u6210\u5206\u304c 0 \u306b\u306a\u308b\u306e\u306f\u3001\u7121\u5fc3\u4e8c\u6b21\u8d85\u66f2\u9762\u306e\u5834\u5408\u306e\u307f\u3067\u3042\u308b\u3002\u4fc2\u6570 1 \u306e\u5358\u4f4d\u884c\u5217\u306e\u6b21\u6570 p \u3068\u3001\u4fc2\u6570 \u22121 \u306e\u5358\u4f4d\u884c\u5217\u306e\u6b21\u6570 q \u3092\u5bfe\u306b\u3057\u305f\u3082\u306e (p, q) \u3092\u3001\u4e8c\u6b21\u8d85\u66f2\u9762\u306e\u7b26\u53f7\u6570\u3068\u3044\u3046\u3002\u4e8c\u6b21\u8d85\u66f2\u9762\u306e\u5f62\u614b\u306f\u3001\u7b26\u53f7\u6570\u306b\u3088\u3063\u3066\u3055\u3089\u306b\u7d30\u304b\u304f\u5206\u985e\u3055\u308c\u308b\u3002Table of Contents\u6955\u5186\u4f53\u306e\u4f53\u7a4d[\u7de8\u96c6]2\u6b21\u5143\u4e8c\u6b21\u66f2\u9762[\u7de8\u96c6]\u4e8c\u6b21\u66f2\u9762\u306e\u5b9f\u7528\u4f8b[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u6955\u5186\u4f53\u306e\u4f53\u7a4d[\u7de8\u96c6]\u7b26\u53f7\u6570\u304c (n, 0) \u3067\u3042\u308b\u3088\u3046\u306a\u4e8c\u6b21\u8d85\u66f2\u9762\u3092\u6955\u5186\u9762\u3068\u3044\u3046\u3002\u6955\u5186\u9762\u306f\u3001\u4e8c\u6b21\u8d85\u66f2\u9762\u306e\u4e2d\u3067\u552f\u4e00\u306e\u9589\u3058\u305f\u8d85\u66f2\u9762\u3067\u3042\u308b\u3002\u5f93\u3063\u3066\u3001\u6955\u5186\u9762\u306b\u3088\u3063\u3066\u56f2\u307e\u308c\u305f\u90e8\u5206\uff08\u6955\u5186\u4f53\uff09\u306b\u306e\u307f\u4f53\u7a4d\u304c\u5b9a\u7fa9\u3067\u304d\u308b\u3002\u305d\u306e\u4f53\u7a4d V \u306f\u3001\u30ac\u30f3\u30de\u95a2\u6570 \u0393(x) \u3092\u7528\u3044\u3066\u3001V=\u0393(1\/2)n\u0393(n\/2+1)1|A|{displaystyle V={frac {Gamma (1\/2)^{n}}{Gamma (n\/2+1)}}{sqrt {frac {1}{|A|}}}}\u3067\u4e0e\u3048\u3089\u308c\u308b\u3002\u3053\u308c\u306f\u534a\u5f84 r \u306e\u7403\u306e\u4f53\u7a4d (4\u03c0\/3)r3 \u306e\u4e00\u822c\u5316\u3067\u3042\u308b\u30022\u6b21\u5143\u4e8c\u6b21\u66f2\u9762[\u7de8\u96c6]\u6bd4\u8f03\u7684\u521d\u7b49\u306e\u6570\u5b66\u3067\u306f\u3001\u4e8c\u6b21\u66f2\u9762\u3068\u8a00\u3046\u3068\u72ed\u7fa9\u306b 3 \u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593 R3 \u5185\u306e\u66f2\u9762\u3092\u6307\u3057\u3066\u3044\u305f\u3002\u305d\u306e\u5b9f\u614b\u306b\u3064\u3044\u3066\u306f\u4e00\u822c\u6b21\u5143\u306e\u5834\u5408\u3068\u540c\u3058\u3067\u3042\u308b\u304c\u3001\u5186\u9310\u66f2\u7dda\u306e\u3088\u3046\u306b\u3001\u5404\u66f2\u9762\u306b\u56fa\u6709\u306e\u540d\u79f0\u304c\u3064\u3044\u3066\u3044\u308b\u306e\u3067\u3001\u305d\u308c\u306b\u3064\u3044\u3066\u6319\u3052\u308b\u3053\u3068\u306b\u3059\u308b\u3002\u3053\u3053\u3067\u306f\u3001a,b,c\u306f\u305d\u308c\u305e\u308c\u6b63\u306e\u5b9f\u6570\u3068\u3059\u308b\u3002\u5b9a\u66f2\u7dda\u306b\u6cbf\u3063\u3066\u76f4\u7dda\u3067\u5f62\u6210\u3055\u308c\u308b\u66f2\u9762\uff08\u7dda\u7e54\u9762\uff09\u306f\u4ee5\u4e0b\u306e4\u901a\u308a\u3067\u3042\u308b\u3002\u9310\u9762\uff08\u5b9f\u306e\u4e8c\u6b21\u9310\u9762\uff09\u53cc\u66f2\u653e\u7269\u9762\u4e00\u8449\u53cc\u66f2\u9762\u67f1\u9762\u203b\u5b9a\u66f2\u7dda\u3068\u925b\u76f4\u306e\u76f4\u7dda\u3067\u5f62\u6210\u3055\u308c\u308b\u3002\u4e8c\u6b21\u66f2\u9762\u306f\u3001xyz-\u7a7a\u9593 R3 \u4e0a\u3067\u5b9a\u7fa9\u3055\u308c\u3001\u6b21\u306e\u9670\u95a2\u6570\u66f2\u7dda\u306b\u3088\u3063\u3066\u4e0e\u3048\u308b\u3053\u3068\u304c\u51fa\u6765\u308b\u3002Q={(x,y,z)\u2208R3\u2223Ax2+By2+Cz2+Dxy+Eyz+Fxz+Gx+Hy+Iz+J=0}{displaystyle Q=left{(x,y,z)in mathbb {R} ^{3}mid Ax^{2}+By^{2}+Cz^{2}+Dxy+Eyz+Fxz+Gx+Hy+Iz+J=0right}}\u03c1(\u203b)\u7b26\u53f7\u6570\u66f2\u9762\u306e\u540d\u79f0\u6a19\u6e96\u5f620\u9310\u9762aX2 + bY2 + cZ2 = 0 \uff08\u4e00\u70b9\u53c8\u306f\u865a\u306e\u4e8c\u6b21\u9318\u9762\uff09aX2 + bY2 \u2212 cZ2 = 01(3, 0)\u6955\u5186\u9762aX2 + bY2 + cZ2 = 11(2, 1)\u4e00\u8449\u53cc\u66f2\u9762aX2 + bY2 \u2212 cZ2 = 11(1, 2)\u4e8c\u8449\u53cc\u66f2\u9762aX2 \u2212 bY2 \u2212 cZ2 = 11(0, 3)\uff08\u306a\u3057\uff09\u53c8\u306f\u865a\u306e\u6955\u5186\u9762\u2212aX2 \u2212 bY2 \u2212 cZ2 = 12(2, 0)\u6955\u5186\u653e\u7269\u9762aX2 + bY2 + 2cZ = 12(1, 1)\u53cc\u66f2\u653e\u7269\u9762aX2 \u2212 bY2 + 2cZ = 12(0, 2)\u6955\u5186\u653e\u7269\u9762\u2212aX2 \u2212 bY2 + 2cZ = 1(R2) 0\u4ea4\u5dee\u4e8c\u5e73\u9762aX2 + bY2 = 0\uff08\u76f4\u7dda\uff09aX2 \u2212 bY2 = 0(R2) 1(2, 0)\u6955\u5186\u67f1\u9762aX2 + bY2 = 1(R2) 1(1, 1)\u53cc\u66f2\u67f1\u9762aX2 \u2212 bY2 = 1(R2) 1(0, 2)\uff08\u306a\u3057\uff09\u53c8\u306f\u865a\u306e\u6955\u5186\u67f1\u9762\u2212aX2 \u2212 bY2 = 1(R2) 2(1, 0)\u653e\u7269\u7dda\u67f1\u9762aX2 + 2bY = 1(R2) 2(0, 1)\u653e\u7269\u7dda\u67f1\u9762\u2212aX2 + 2bY = 1(R1) 0\u91cd\u306a\u3063\u305f\u4e8c\u5e73\u9762aX2 = 0(R1) 1(1, 0)\u5e73\u884c\u4e8c\u5e73\u9762aX2 = 1(R1) 1(0, 1)\uff08\u306a\u3057\uff09\u53c8\u306f\u5e73\u884c\u306a\u865a\u306e\u4e8c\u5e73\u9762\u2212aX2 = 1\u203b \u03c1 = rank R \u2212 rank A 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