[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/229#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/229","headline":"Quadrik  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"Quadrik  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u4e00 Quadrik \uff08\u304b\u3089 \u30e9\u30c6\u30f3 \u30d6\u30ed\u30c3\u30af Quadrat\uff09\u306f\u3001\u6570\u5b66\u306b\u304a\u3051\u308b\u6570\u4eba\u306e\u898b\u77e5\u3089\u306c\u4eba\u306e\u5e73\u65b9\u65b9\u7a0b\u5f0f\u306e\u6eb6\u6db2\u91cf\u3067\u3059\u3002 2\u6b21\u5143\u3067\u306f\u3001\u901a\u5e38\u3001\u30af\u30ef\u30c9\u30ea\u30af\u306f\u30ec\u30d9\u30eb\u306b\u66f2\u7dda\u3092\u5f62\u6210\u3057\u3001\u30b3\u30fc\u30f3\u30ab\u30c3\u30c8\u3067\u3059\u3002 3\u6b21\u5143\u3067\u306f\u3001\u30af\u30ef\u30c9\u30ea\u30af\u306f\u901a\u5e38\u3001\u90e8\u5c4b\u306e\u9818\u57df\u3092\u8aac\u660e\u3057\u307e\u3059\u3002 2\u6b21\u306e\u30a8\u30ea\u30a2 \u307e\u305f \u6b63\u65b9\u5f62\u306e\u9818\u57df \u547c\u3070\u308c\u3066\u3044\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\u30af\u30ef\u30c9\u30ea\u30af\u306f\u3001\u6700\u7d42\u7684\u306b\u5bf8\u6cd5\u306e\u5b9f\u969b\u306e\u5ea7\u6a19\u9818\u57df\u306b\u3042\u308b\u4ee3\u6570\u7684\u306a\u54c1\u7a2e\u3001\u3064\u307e\u308a\u7279\u5225\u306a\u30cf\u30a4\u30d1\u30fc\u30d5\u30a7\u30a4\u30b9\u3067\u3059\u3002\u30e1\u30a4\u30f3\u30a2\u30af\u30b9\u30eb\u5909\u63db\u306b\u3088\u308a\u3001\u5404\u56db\u65b9\u6027\u306f\u3001\u53ef\u80fd\u306a3\u3064\u306e\u901a\u5e38\u306e\u5f62\u5f0f\u306e\u3044\u305a\u308c\u304b\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001Quadriken\u306f\u3055\u307e\u3056\u307e\u306a\u57fa\u672c\u30bf\u30a4\u30d7\u306b\u5206\u985e\u3067\u304d\u307e\u3059\u3002 after-content-x4 Quadriken\u306f\u3001\u7279\u306b\u5206\u6790\u7684\u304a\u3088\u3073\u5c04\u5f71\u5e7e\u4f55\u5b66\u3067\u8abf\u3079\u3089\u308c\u307e\u3059\u3002\u30c6\u30af\u30ce\u30ed\u30b8\u30fc\u3068\u81ea\u7136\u79d1\u5b66\u306b\u304a\u3051\u308b\u56db\u89d2\u5316\u306e\u7528\u9014\u306f\u3001\u6e2c\u5730\u57fa\u6e96\uff08\u53c2\u7167\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0\uff09\u3001\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\uff08\u69cb\u9020\u5de5\u5b66\uff09\u3001\u307e\u305f\u306f\u5149\u5b66\u7cfb\uff08\u653e\u7269\u7dda\u30ec\u30d9\u30eb\uff09\u306b\u3042\u308a\u307e\u3059\u3002 \u305d\u308c\u305e\u308c\u306e\u30af\u30a2\u30c9\u30ea\u30c3\u30af\u3001d\u3002 H.\u89e3\u6c7a\u7b56\u306f\u3001\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 Q {\u30c6\u30ad\u30b9\u30c8\u30b9\u30bf\u30a4\u30ebQ} \u5c02\u7528\u3002\u3055\u3089\u306b\u3001\u3053\u306e\u30da\u30fc\u30b8\u3067\u6b21\u306e\u8868\u8a18\u3092\u4f7f\u7528\u3057\u3066\u3001\u7dda\u5f62\u4ee3\u6570\u3067\u4f7f\u7528\u3055\u308c\u308b\u30b7\u30f3\u30dc\u30eb\u3092\u533a\u5225\u3057\u307e\u3059\u3002","datePublished":"2022-02-19","dateModified":"2022-02-19","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?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\/3\/39\/Quadriken-7.svg\/300px-Quadriken-7.svg.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/39\/Quadriken-7.svg\/300px-Quadriken-7.svg.png","height":"196","width":"300"},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/229","wordCount":13660,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4 \u4e00 Quadrik \uff08\u304b\u3089 \u30e9\u30c6\u30f3  \u30d6\u30ed\u30c3\u30af Quadrat\uff09\u306f\u3001\u6570\u5b66\u306b\u304a\u3051\u308b\u6570\u4eba\u306e\u898b\u77e5\u3089\u306c\u4eba\u306e\u5e73\u65b9\u65b9\u7a0b\u5f0f\u306e\u6eb6\u6db2\u91cf\u3067\u3059\u3002 2\u6b21\u5143\u3067\u306f\u3001\u901a\u5e38\u3001\u30af\u30ef\u30c9\u30ea\u30af\u306f\u30ec\u30d9\u30eb\u306b\u66f2\u7dda\u3092\u5f62\u6210\u3057\u3001\u30b3\u30fc\u30f3\u30ab\u30c3\u30c8\u3067\u3059\u3002 3\u6b21\u5143\u3067\u306f\u3001\u30af\u30ef\u30c9\u30ea\u30af\u306f\u901a\u5e38\u3001\u90e8\u5c4b\u306e\u9818\u57df\u3092\u8aac\u660e\u3057\u307e\u3059\u3002 2\u6b21\u306e\u30a8\u30ea\u30a2 \u307e\u305f \u6b63\u65b9\u5f62\u306e\u9818\u57df \u547c\u3070\u308c\u3066\u3044\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\u30af\u30ef\u30c9\u30ea\u30af\u306f\u3001\u6700\u7d42\u7684\u306b\u5bf8\u6cd5\u306e\u5b9f\u969b\u306e\u5ea7\u6a19\u9818\u57df\u306b\u3042\u308b\u4ee3\u6570\u7684\u306a\u54c1\u7a2e\u3001\u3064\u307e\u308a\u7279\u5225\u306a\u30cf\u30a4\u30d1\u30fc\u30d5\u30a7\u30a4\u30b9\u3067\u3059\u3002\u30e1\u30a4\u30f3\u30a2\u30af\u30b9\u30eb\u5909\u63db\u306b\u3088\u308a\u3001\u5404\u56db\u65b9\u6027\u306f\u3001\u53ef\u80fd\u306a3\u3064\u306e\u901a\u5e38\u306e\u5f62\u5f0f\u306e\u3044\u305a\u308c\u304b\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001Quadriken\u306f\u3055\u307e\u3056\u307e\u306a\u57fa\u672c\u30bf\u30a4\u30d7\u306b\u5206\u985e\u3067\u304d\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Quadriken\u306f\u3001\u7279\u306b\u5206\u6790\u7684\u304a\u3088\u3073\u5c04\u5f71\u5e7e\u4f55\u5b66\u3067\u8abf\u3079\u3089\u308c\u307e\u3059\u3002\u30c6\u30af\u30ce\u30ed\u30b8\u30fc\u3068\u81ea\u7136\u79d1\u5b66\u306b\u304a\u3051\u308b\u56db\u89d2\u5316\u306e\u7528\u9014\u306f\u3001\u6e2c\u5730\u57fa\u6e96\uff08\u53c2\u7167\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0\uff09\u3001\u30a2\u30fc\u30ad\u30c6\u30af\u30c1\u30e3\uff08\u69cb\u9020\u5de5\u5b66\uff09\u3001\u307e\u305f\u306f\u5149\u5b66\u7cfb\uff08\u653e\u7269\u7dda\u30ec\u30d9\u30eb\uff09\u306b\u3042\u308a\u307e\u3059\u3002 \u305d\u308c\u305e\u308c\u306e\u30af\u30a2\u30c9\u30ea\u30c3\u30af\u3001d\u3002 H.\u89e3\u6c7a\u7b56\u306f\u3001\u6b21\u306e\u3068\u304a\u308a\u3067\u3059 Q {\u30c6\u30ad\u30b9\u30c8\u30b9\u30bf\u30a4\u30ebQ} \u5c02\u7528\u3002\u3055\u3089\u306b\u3001\u3053\u306e\u30da\u30fc\u30b8\u3067\u6b21\u306e\u8868\u8a18\u3092\u4f7f\u7528\u3057\u3066\u3001\u7dda\u5f62\u4ee3\u6570\u3067\u4f7f\u7528\u3055\u308c\u308b\u30b7\u30f3\u30dc\u30eb\u3092\u533a\u5225\u3057\u307e\u3059\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4a {displaystyle a} \u5b9f\u6570\u3092\u8868\u3057\u307e\u3059\u3001 a {displaystyle mathrm {a}} \u30d9\u30af\u30c8\u30eb\uff08\u5c0f\u3055\u306a\u6587\u5b57\u3067\u76f4\u7acb\uff09\u3001 a {displaystyle mathrm {a}} \u30de\u30c8\u30ea\u30c3\u30af\u30b9\uff08\u5927\u6587\u5b57\u3067\u76f4\u7acb\uff09\u3002        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u30af\u30a2\u30c9\u30ea\u30c3\u30af\u306f\u30dd\u30a4\u30f3\u30c8\u91cf\u3067\u3059 n {displaystyle n}  – \u6b21\u5143\u306e\u5b9f\u969b\u306e\u5ea7\u6a19\u7a7a\u9593 r n {displaystyle mathbb {r} ^{n}} \u30d5\u30a9\u30fc\u30e0 Q = { (x1,\u2026,xn)\u2208Rn\u2223q(x1,\u2026,xn)=0} {displaystyle q = left {\uff08x_ {1}\u3001ldots\u3001x_ {n}\uff09in mathbb {r} ^{n} mid q\uff08x_ {1}\u3001ldots\u3001x_ {n}\uff09= 0right}}} \u3001 \u3057\u305f\u304c\u3063\u3066 Q \uff08 \u30d0\u30c4 1\u3001 … \u3001 \u30d0\u30c4 n\uff09\uff09 = \u2211 i,j=1na ij\u30d0\u30c4 i\u30d0\u30c4 j+ 2 \u2211 i=1nb i\u30d0\u30c4 i+ c {displaystyle q\uff08x_ {1}\u3001ldots\u3001x_ {n}\uff09= sum _ {i\u3001j = 1}^{n} a_ {ij} x_ {i} x_ {j}+2\u3001sum _ {i = 1}^{n} \u5909\u6570\u306e\u6b63\u65b9\u5f62\u591a\u9805\u5f0f \u30d0\u30c4 \u521d\u3081 \u3001 … \u3001 \u30d0\u30c4 n {displaystyle x_ {1}\u3001ldots\u3001x_ {n}} \u306f\u3002\u591a\u9805\u5f0f\u4fc2\u6570\u306e\u5c11\u306a\u304f\u3068\u30821\u3064 a 11 \u3001 … \u3001 a n n {displaystyle a_ {11}\u3001dots\u3001a_ {nn}} \u306f\u308b\u304b\u306b\u30bc\u30ed\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u3055\u3089\u306b\u3001\u5236\u9650\u306a\u3057\u306b\u60f3\u5b9a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 a \u79c1 j = a j \u79c1 {displaystyle a_ {ij} = a_ {ji}} \u3059\u3079\u3066\u306e\u305f\u3081\u306b \u79c1 \u3001 j \u2208 { \u521d\u3081 \u3001 … \u3001 n } {displaystyle I\u3001jin {1\u3001dotsc\u3001n}} \u9069\u7528\u53ef\u80fd\u3067\u3059\u3002\u56db\u65b9\u7684\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u5909\u6570\u306e\u6b63\u65b9\u5f62\u591a\u9805\u5f0f\u306e\u30bc\u30ed\u91cf\u307e\u305f\u306f\u3044\u304f\u3064\u304b\u306e\u898b\u77e5\u3089\u306c\u4eba\u3068\u306e\u6eb6\u6db2\u91cf\u306e\u6eb6\u6db2\u91cf\u3067\u3059\u3002 \u305f\u3068\u3048\u3070\u3001\u30dd\u30a4\u30f3\u30c8\u306e\u91cf\u304c\u8a18\u8ff0\u3055\u308c\u307e\u3059 Q = { (x,y)\u2208R2\u22232x2+3y2=5} {displaystyle q = left {\uff08x\u3001y\uff09in mathbb {r}^{2} mid 2x^{2}+3y^{2} = 5right}} \u30ec\u30d9\u30eb\u306e\u6955\u5186\u3002\u30dd\u30a4\u30f3\u30c8\u306e\u91cf Q = { (x,y,z)\u2208R3\u2223x2+y2\u2212z2=1} {displaystyle q = left {\uff08x\u3001y\u3001z\uff09in mathbb {r}^{3} mid x^{2}+y^{2} -z^{2} = 1 right}}} 3\u6b21\u5143\u7a7a\u9593\u306b\u3042\u308b\u5358\u4e00\u306e\u5b57\u578b\u53cc\u66f2\u7dda\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002 Table of Contents\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30bf\u30a4\u30d7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u5909\u63db [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u901a\u5e38\u306e\u30d5\u30a9\u30fc\u30e0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u6b21\u5143\u306eQuadriken [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30ec\u30d9\u30eb\u306eQuadriken [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u90e8\u5c4b\u306eQuadriken [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30de\u30c8\u30ea\u30c3\u30af\u30b9\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u8868\u8a18\u3067\u306f\u3001\u30af\u30c9\u30ea\u30c3\u30af\u306f\u591a\u304f\u306e\u30d9\u30af\u30c8\u30eb\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059 Q = { x\u2208Rn\u2223xTAx+2bTx+c=0} {displaystyle q = left {mathrm {x} in mathbb {r}^{n} mid mathrm {x^{t}} mathrm {a} mathrm {xrm {b^{t}}} mathrm {x} + \u8aac\u660e\u3057\u3066\u304f\u3060\u3055\u3044 a = \uff08 a \u79c1 j \uff09\uff09 \u2208 r n \u00d7 n {displaystyle mathrm {a} =\uff08a_ {ij}\uff09in mathbb {r} ^{ntimes n}} \u5bfe\u79f0\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3068 b = \uff08 b \u79c1 \uff09\uff09 \u2208 r n {displaystyle mathrm {b} =\uff08b_ {i}\uff09in mathbb {r} ^{n}} \u3068\u3057\u3066\u3082  \u30d0\u30c4 = \uff08 \u30d0\u30c4 \u79c1 \uff09\uff09 \u2208 r n {displaystyle mathrm {x} =\uff08x_ {i}\uff09in mathbb {r} ^{n}} \u5217\u30d9\u30af\u30c8\u30eb\u306f\u5bfe\u5fdc\u3059\u308b\u9577\u3055\u3067\u3059\u3002\u62e1\u5f35\u30d7\u30ec\u30bc\u30f3\u30c6\u30fc\u30b7\u30e7\u30f3\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u52a9\u3051\u3092\u501f\u308a\u3066 A\u00af= (AbbTc){displaysyllle mathrm {bar {pmatrix} = {begin {pmatrix} mathrm {a}\uff06mathrm {b ^ {t {t}\uff06cend {pmatrix} … \u305d\u308c\u306b\u5fdc\u3058\u3066\u30d9\u30af\u30c8\u30eb\u3092\u62e1\u5f35\u3057\u307e\u3057\u305f x\u00af= (x1){displaystyle mathrm {bar {x}} = {tbinom {mathrm {x}} {1}}}} \u30af\u30a2\u30c9\u30ea\u30c3\u30af\u306f\u30b3\u30f3\u30d1\u30af\u30c8\u306b\u30b3\u30f3\u30d1\u30af\u30c8\u306b\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059 Q = { x\u2208Rn\u2223x\u00afTA\u00afx\u00af=0} {displaystyle q = left {mathrm {x} in mathbb {r} ^{n} mid mathrm {{bar {x}} ^{t}} mathrm {ar {a}}\u3001mathrm {x} = 0right}}}} \u5747\u4e00\u306a\u5ea7\u6a19\u3067\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \u30bf\u30a4\u30d7 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] Quadriken\u30673\u3064\u306e\u57fa\u672c\u7684\u306a\u30bf\u30a4\u30d7\u304c\u533a\u5225\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3069\u306e\u30bf\u30a4\u30d7\u304c\u4e0e\u3048\u3089\u308c\u305fQuadrika\u3067\u3042\u308b\u304b\u306f\u3001\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u30e9\u30f3\u30af\u306b\u57fa\u3065\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059 a {displaystyle mathrm {a}} \u3001 \uff08 a | b \uff09\uff09 {displaystyle\uff08mathrm {a | b}\uff09} \u3068 A\u00af{displaystyle mathrm {bar {a}}} \u30d2\u30c3\u30c8\u3059\u308b\uff1a [\u521d\u3081] \u30b5\u30f3\u30c0\u30fc\u306e\u30bf\u30a4\u30d7 \uff1a \u30ed\u30fc\u30b9\u30c8 \u2061 \uff08 A\u00af\uff09\uff09 = \u30ed\u30fc\u30b9\u30c8 \u2061 \uff08 a |b \uff09\uff09 = \u30ed\u30fc\u30b9\u30c8 \u2061 \uff08 a \uff09\uff09 {displaystyle operatorname {rang}\uff08operatorname {rang}\uff08operatorname}\uff08operatorame {rang}\uff08mathrm {a}\uff09\uff09 \u30bb\u30f3\u30bf\u30fcQuadrika \uff1a "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/229#breadcrumbitem","name":"Quadrik  – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]