[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/4664#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/4664","headline":"\u30dc\u30c7\u30a3\u4e0a\u306e\u4ee3\u6570 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","name":"\u30dc\u30c7\u30a3\u4e0a\u306e\u4ee3\u6570 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2","description":"before-content-x4 \u4e00 \u4f53\u306e\u4ee3\u6570 k {displaystyle k} after-content-x4 \u3001 \u4ee3\u6570\u30aa\u30fc\u30d0\u30fc k {displaystyle k} \u307e\u305f k {displaystyle k} -\u4ee3\u6570 \uff08\u4ee5\u524d\u3082 \u7dda\u5f62\u4ee3\u6570 \u5c02\u7528\uff09","datePublished":"2020-04-19","dateModified":"2020-04-19","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:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/2b76fce82a62ed5461908f0dc8f037de4e3686b0","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/2b76fce82a62ed5461908f0dc8f037de4e3686b0","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki11\/archives\/4664","wordCount":10466,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4\u4e00 \u4f53\u306e\u4ee3\u6570 k {displaystyle k}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u3001 \u4ee3\u6570\u30aa\u30fc\u30d0\u30fc k {displaystyle k} \u307e\u305f k {displaystyle k} -\u4ee3\u6570 \uff08\u4ee5\u524d\u3082 \u7dda\u5f62\u4ee3\u6570 \u5c02\u7528\uff09 [\u521d\u3081] \u4f53\u306e\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u5ba4\u3067\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4k {displaystyle k} \u3001\u30d9\u30af\u30bf\u30fc\u306e\u69cb\u9020\u3068\u4e92\u63db\u6027\u306e\u3042\u308b\u4e57\u7b97\u3092\u542b\u3080\u3088\u3046\u306b\u62e1\u5f35\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u306b\u5fdc\u3058\u3066\u3001\u4e57\u7b97\u304c\u9023\u60f3\u884c\u70ba\u307e\u305f\u306f\u901a\u52e4\u6cd5\u3092\u6e80\u305f\u3059\u3053\u3068\u3082\u3001\u4ee3\u6570\u304c\u4e57\u7b97\u306b\u95a2\u3057\u3066\u518d\u8981\u7d20\u3092\u6301\u3063\u3066\u3044\u308b\u3053\u3068\u3082\u5fc5\u8981\u3067\u3059\u3002 \u4e00 \u4ee3\u6570  a {displaystyle a} \u4f53\u306e\u4e0a k {displaystyle k} \u307e\u305f\u306f\u77ed\u3044        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4k {displaystyle k}  – \u4ee3\u6570\u306f1\u3064\u3067\u3059 k {displaystyle k} -1\u3064\u306e\u30d9\u30af\u30c8\u30eb\u30eb\u30fc\u30e0 k {displaystyle k}  – \u4e8c\u91cd\u30ea\u30f3\u30af a \u00d7 a \u2192 a \u3001 {displaystyle atimes ato a\u3001} \u30b9\u30eb\u30fc\u3092\u547c\u3073\u51fa\u3059\u4e57\u7b97 \u30d0\u30c4 de \u3068 {displaystyle xcdot y} \u307e\u305f \u30d0\u30c4 \u3068 {displaystyle xy} \u8c61\u5fb4\u3055\u308c\u3066\u3044\u307e\u3059\u3002 \uff08\u3053\u306e\u30ea\u30f3\u30af\u306f\u3001\u4f53\u5185\u306e\u4e57\u7b97\u3068\u30d9\u30af\u30c8\u30eb\u3092\u6301\u3064\u8eab\u4f53\u8981\u7d20\u306e\u30ea\u30f3\u30af\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3059\u3002\u540c\u3058\u30b7\u30f3\u30dc\u30eb\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u304c\u3069\u306e\u30ea\u30f3\u30af\u304c\u610f\u5473\u3059\u308b\u304b\u3092\u793a\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u6df7\u4e71\u306b\u3064\u306a\u304c\u308a\u307e\u305b\u3093\u3002\uff09 \u4e21\u7dda\u5f62\u306f\u3001\u3059\u3079\u3066\u306e\u8981\u7d20\u306b\u5bfe\u3057\u3066\u660e\u793a\u7684\u306b\u305d\u308c\u3092\u610f\u5473\u3057\u307e\u3059 \u30d0\u30c4 \u3001 \u3068 \u3001 \u3068 \u2208 a {displaystyle x\u3001y\u3001zin a} \u305d\u3057\u3066\u3059\u3079\u3066\u306e\u30b9\u30b1\u30fc\u30e9 l \u2208 k {displaystyle lambda in k} \u8a72\u5f53\u3059\u308b\uff1a \uff08 \u30d0\u30c4 + \u3068 \uff09\uff09 de \u3068 = \u30d0\u30c4 de \u3068 + \u3068 de \u3068 {displaystyle\uff08x+y\uff09cdot z = xcdot z+ycdot z} \u30d0\u30c4 de \uff08 \u3068 + \u3068 \uff09\uff09 = \u30d0\u30c4 de \u3068 + \u30d0\u30c4 de \u3068 {displaystyle xcdot\uff08y+z\uff09= xcdot y+xcdot z} l \uff08 \u30d0\u30c4 de \u3068 \uff09\uff09 = \uff08 l \u30d0\u30c4 \uff09\uff09 de \u3068 = \u30d0\u30c4 de \uff08 l \u3068 \uff09\uff09 {displaystyle lambda\uff08xcdot y\uff09=\uff08lambda x\uff09cdot y = xcdot\uff08lambda y\uff09} \u57fa\u790e\u3068\u306a\u308b\u8eab\u4f53\u306f\u5b9f\u6570\u306e\u4f53\u3067\u3059 r {displaystyle mathbb {r}} \u3001\u4ee3\u6570\u306f\u672c\u7269\u306e\u4ee3\u6570\u3068\u3082\u547c\u3070\u308c\u307e\u3059\u3002 [2] \u306e\u6982\u5ff5 k {displaystyle k} -\u4ee3\u6570 \u30dc\u30c7\u30a3\u3092\u901a\u52e4\u30ea\u30f3\u30b0\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 r {displaystyle r} -\u4ee3\u6570 \u3001\u901a\u52e4\u30ea\u30f3\u30b0\u306e\u4e0a\u306e\u4ee3\u6570\u3002\u5b9a\u7fa9\u3067\u306f\u3001\u300c\u30d9\u30af\u30c8\u30eb\u30eb\u30fc\u30e0\u300d\u3092\u300c\u30e2\u30b8\u30e5\u30fc\u30eb\u300d\u3068\u4ea4\u63db\u3067\u304d\u307e\u3059\u3002 \u4e00 \u975e\u59d4\u54e1 \u306e {displaystyleu} \u4ee3\u6570 a {displaystyle a} \u4f53\u306e\u4e0a k {displaystyle k} \u306e\u30b5\u30d6\u30b9\u30da\u30fc\u30b9\u3067\u3059 a {displaystyle a} \u3001\u8ab0\u304c\u3001\u30b9\u30ab\u30e9\u30fc\u3067\u52a0\u7b97\u3068\u4e57\u7b97\u306b\u52a0\u3048\u3066\u3001\u306e\u8981\u7d20\u3067\u3042\u308b k {displaystyle k} \u3001in\u306e\u4e0b\u3067\u3082 a {displaystyle a} \u5b9a\u7fa9\u3055\u308c\u305f\u4e57\u7b97\u304c\u5b8c\u4e86\u3057\u307e\u3059\u3002 H. \u306e \u3001 \u306e \u2208 \u306e \u21d2 \u306e \u306e \u2208 \u306e {displaystyle u\u3001vin urightarrow uvin u} \u3002\u305d\u308c\u304b\u3089 \u306e {displaystyleu} \u72ec\u7acb\u3057\u305f\u4ee3\u6570\u3002\u8907\u96d1\u306a\u6570\u5024\u3092\u5b9f\u969b\u306e\u4ee3\u6570\u3068\u3057\u3066\u3001\u305f\u3068\u3048\u3070\u5b9f\u969b\u306e\u4ee3\u6570\u3068\u3057\u3066\u914d\u7f6e\u3059\u308b\u5834\u5408\u3001\u60f3\u50cf\u4e0a\u306e\u6570\u5b57\u3067\u306f\u306a\u304f\u3001\u8907\u96d1\u306a\u6570\u5b57\u306e\u4e0b\u4f4d\u4ee3\u6570\u3092\u5f62\u6210\u3057\u307e\u3059\u3002 \u305d\u308c\u3092\u8d85\u3048\u3066\u3044\u307e\u3059 \u306e \u2208 \u306e \u21d2 a \u306e \u2208 \u306e {displaystyle vin urightarrow avin u} \u4efb\u610f\u306e\u8981\u7d20\u3067 a {displaystyle a} \u304b\u3089 a {displaystyle a} \u3001\u547c\u3070\u308c\u307e\u3059 \u306e {displaystyleu} \u306e\u5de6\u5074\u306e\u7406\u60f3 a {displaystyle a} \u3002\u3057\u305f\u304c\u3063\u3066\u3001\u610f\u5473\u304c\u3042\u308a\u307e\u3059 \u306e {displaystyleu} \u3001\u6edd \u306e \u2208 \u306e \u21d2 \u306e a \u2208 \u306e {displaystyle vin urightarrow vain u} \u53f3\u5074\u306e\u7406\u60f3 a {displaystyle a} \u306f\u3002\u5834\u5408\u3067\u3082\u305d\u3046\u3067\u3059 a {displaystyle a} \u901a\u52e4\u3001\u305d\u308c\u306f\u610f\u5473\u3057\u307e\u3059 \u306e {displaystyleu} \u5358\u306b\u7406\u60f3\u3067\u3059 a {displaystyle a} \u3002\u4ee3\u6570\u306e\u5834\u5408 a {displaystyle a} \u81ea\u660e\u3067\u306a\u3044\u7406\u60f3\u306f\u3042\u308a\u307e\u305b\u3093\u3001\u305d\u308c\u306f\u547c\u3070\u308c\u3066\u3044\u307e\u3059 \u5358\u306b \u3002 Table of Contents\u9023\u60f3\u30a2\u30eb\u30d0\u30e9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30a2\u30eb\u30d0\u30fc\u30b9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30e6\u30cb\u30bf\u30ea\u30a2\u30f3\u30fb\u30a2\u30eb\u30d0\u30e9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u95a2\u9023\u3057\u3066\u3044\u306a\u3044\u30a2\u30eb\u30d0\u30e9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u9023\u60f3\u30a2\u30eb\u30d0\u30e9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u9023\u60f3\u4ee3\u6570\u306f1\u3064\u3067\u3059 k {displaystyle k} -albra\u3001\u95a2\u9023\u3059\u308b\u884c\u70ba\u306f\u4e57\u7b97\u306b\u9069\u7528\u3055\u308c\u308b\u305f\u3081\u3001\u30ea\u30f3\u30b0\u3067\u3059\u3002\u4f8b\uff1a \u306e\u4ee3\u6570 n \u00d7 n {displaystyle n}  – \u4f53\u306e\u4e0a\u306e\u30de\u30c8\u30ea\u30b8\u30f3\u3002\u4e57\u7b97\u306f\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u4e57\u7b97\u3067\u3059\u3002 \u90e8\u5206\u7684\u306b\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u91d1\u984d\u306e\u767a\u751f\u7387\u30a2\u30eb\u30d0\u30e0\u3002 1\u3064\u306e\u7dda\u5f62\u6f14\u7b97\u5b50\u306e\u30a2\u30eb\u30d0\u30fc k {displaystyle k} -Vektorraum\u81ea\u4f53\u3002\u3053\u3053\u3067\u306e\u4e57\u7b97\u306f\u7d99\u627f\u3067\u3059\u3002\u4ee3\u6570\u306f\u3001\u305d\u308c\u304c\u30de\u30c8\u30ea\u30af\u30b7\u30e3\u30eb\u30d6\u30e9\u3078\u306e\u540c\u578b\u3067\u3042\u308b\u5834\u5408\u3001\u6e1b\u8870\u3068\u547c\u3070\u308c\u307e\u3059\u3002 \u30b0\u30eb\u30fc\u30d7\u4ee3\u6570 k [ g ] {displaystyle k [g]} \u30b0\u30eb\u30fc\u30d7\u306b g {displaystyle g} ;\u3053\u3053\u3067\u3001\u30b0\u30eb\u30fc\u30d7\u8981\u7d20\u306fa\u3092\u5f62\u6210\u3057\u307e\u3059 k {displaystyle k} -basis des k {displaystyle k}  – \u30d9\u30af\u30c8\u30eb\u30b9\u30da\u30fc\u30b9 k [ g ] {displaystyle k [g]} \u3001\u305d\u3057\u3066\u4ee3\u6570\u306e\u4e57\u7b97\u306f\u3001\u30b0\u30eb\u30fc\u30d7\u4e57\u7b97\u306e\u53cc\u7dda\u5f62\u306e\u7d99\u7d9a\u3067\u3059\u3002 \u4ee3\u6570 k [ \u30d0\u30c4 ] {displaystyle k [x]} \u4fc2\u6570\u3092\u6301\u3064\u30dd\u30ea\u30ce\u30fc\u30e0 k {displaystyle k} \u672a\u77e5\u306e \u30d0\u30c4 {displaystyle x} \u3002 \u4ee3\u6570 k [ \u30d0\u30c4 1\u3001 … \u3001 \u30d0\u30c4 n] {displaystyle k [x_ {1}\u3001dotsc\u3001x_ {n}]} \u4fc2\u6570\u3092\u6301\u3064\u30dd\u30ea\u30ce\u30fc\u30e0 k {displaystyle k} \u3044\u304f\u3064\u304b\u306e\u672a\u77e5\u6570\u3067 \u30d0\u30c4 1\u3001 … \u3001 \u30d0\u30c4 n{displaystyle x_ {1}\u3001dotsc\u3001x_ {n}} \u3002 \u4e00 \u6a5f\u80fd\u7684 \u3042\u306a\u305f\u306f\u91cf\u306e\u591a\u304f\u306e\u6a5f\u80fd\u306b\u3088\u3063\u3066\u5f97\u3089\u308c\u307e\u3059 m {displaystyle m} \u4f53\u5185 k {displaystyle k} \u4ee5\u4e0b\u3067 \u30dd\u30a4\u30f3\u30c8\u4e57\u7b97 \u63d0\u4f9b\uff1a (f\u22c5g)(x):=f(x)\u22c5g(x),f,g:M\u2192K,x\u2208M{displaystyle\uff08fcdot g\uff09\uff08x\uff09\uff1a= f\uff08x\uff09cdot g\uff08x\uff09\u3001qquad f\u3001gcolon mto k\u3001xin m} \u3002 \u306e\u8eab\u4f53\u62e1\u5f35 k {displaystyle k} \u9023\u60f3\u4ee3\u6570\u3067\u3059 k {displaystyle k} \u3002 z\u3002 B. r {displaystyle mathbb {r}} \u4e00 Q {displaystyle mathbb {q}}  – \u4ee3\u6570\u3068 c {displaystyle mathbb {c}} \u3067\u304d\u308b Q {displaystyle mathbb {q}}  – \u4ee3\u6570\u307e\u305f\u306fas r {displaystyle mathbb {r}}  – \u4ee3\u6570\u304c\u8003\u616e\u3055\u308c\u307e\u3059\u3002 \u4ee3\u6570 h {displaystyle mathbb {h}} \u30cf\u30df\u30eb\u30c8\u30f3\u306e\u56db\u5143\u6570\u306f\u30014\u6b21\u5143\u306e\u9023\u60f3\u30e6\u30cb\u30bf\u30ea\u30a2\u30f3\u306e\u672c\u7269\u306e\u4ee3\u6570\u3067\u3042\u308a\u3001\u66f2\u304c\u3063\u305f\u4f53\u3068\u3057\u3066\u306e\u5206\u88c2\u30b5\u30eb\u30d6\u30e9\u3067\u3055\u3048\u3042\u308a\u307e\u3059\u3002\u5f7c\u5973\u306f\u6700\u7d42\u7684\u306b\u6b21\u5143\u3067\u3059 \u4e2d\u592e\u306e\u4ee3\u6570 \uff08\u30a2\u30ba\u30de\u30e4\u4ee3\u6570\uff09\u4f53\u306e\u4e0a r {displaystyle mathbb {r}} \u3002\u5b9f\u969b\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3068\u3057\u3066\u3001\u7570\u306a\u308b\u30b3\u30d4\u30fc\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059 \u79c1 \u03f5\uff08 c \uff09\uff09 = r [ \u03f5 ] {displaystyle iota _ {epsilon}\uff08mathbb {c}\uff09= mathbb {r} [epsilon]} \u4f53\u306e c {displaystyle mathbb {c}} \u8907\u96d1\u306a\u6570\u5b57 r {displaystyle mathbb {r}} \u30bb\u30f3\u30bf\u30fc\u3067\u3042\u308b\u5b9f\u6570\u306e\u6570\uff1a h \u228b r [ \u03f5 ] \u228b r = \u3068 \uff08 h \uff09\uff09 {displaystyle mathbb {h} supsetneq mathbb {r} [epsilon] supsetneq mathbb {r} = z\uff08mathbb {h}\uff09}}} \u3002\u8ab0\u3082\u304c\u914d\u9054\u3057\u307e\u3059 \u03f5 \u2208 h {displaystyle epsilon in mathbb {h}} \u3068 \u03f5 2=  –  \u521d\u3081 {displaystyle epsilon ^{2} = -1} \u57cb\u3081\u8fbc\u307f \u79c1 \u03f5\uff1a c \u2192 h {displaystyle iota _ {epsilon}\u30b3\u30ed\u30f3Mathbb {c}\u304b\u3089mathbb {h}}\u3078 \u4f53\u306e c {displaystyle mathbb {c}} \u306e h {displaystyle mathbb {h}} \u3001\u305d\u306e\u7b49\u578b\u306e\u7d75\u306f\u73fe\u5728\u3067\u3059 r [ \u03f5 ] {displaystyle mathbb {r} [epsilon]} \u306f\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u3089\u306e\u57cb\u3081\u8fbc\u307f\u306f\u305d\u308c\u305e\u308c\u5b9f\u969b\u306e\u4ee3\u6570\u3092\u88c5\u5099\u3057\u307e\u3059 h {displaystyle mathbb {h}} \u8907\u96d1\u306a\u30d9\u30af\u30c8\u30eb\u30eb\u30fc\u30e0\u306e\u69cb\u9020\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u306e\u8907\u96d1\u306a\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u69cb\u9020\u306b\u95a2\u9023\u3059\u308b\u56db\u9805\u4ee3\u6570\u306e\u4e57\u7b97\u306f\u53cc\u7dda\u5f62\u3067\u306f\u3042\u308a\u307e\u305b\u3093 c {displaystyle mathbb {c}} \u3001\u3057\u304b\u3057\u3001\u7d42\u308f\u3063\u305f\u3060\u3051\u3067\u3059 \u3068 \uff08 h \uff09\uff09 = r {displaystyle z\uff08mathbb {h}\uff09= mathbb {r}} \u3002\u3057\u305f\u304c\u3063\u3066\u3001Quaternions\u306f\u8907\u96d1\u306a\u4ee3\u6570\u3092\u5f62\u6210\u3057\u307e\u305b\u3093\u3002 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30fc\u30a2\u30eb\u30d0\u30fc\u30b9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e00 Kommutate \u4ee3\u6570\u306f1\u3064\u3067\u3059 k {displaystyle k}  – \u4ee3\u6570\u3001\u901a\u52e4\u884c\u70ba\u306f\u4e57\u7b97\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002\u4f8b\uff1a \u901a\u52e4\u4ee3\u6570\u306e\u6570\u5b66\u7684\u30b5\u30d6\u30a8\u30ea\u30a2\u3067\u306f\u3001Albars\u304c\u9023\u60f3\u7684\u3067\u901a\u52e4\u3059\u308b\u3068\u898b\u306a\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306b\u306f\u3001\u4e0a\u8a18\u306e\u30dd\u30ea\u30ce\u30de\u30eb\u7d50\u5408\u3001\u6a5f\u80fd\u7684\u7d50\u5408\u3001\u8eab\u4f53\u62e1\u5f35\u304c\u542b\u307e\u308c\u307e\u3059\u3002 \u907a\u4f1d\u7684\u30a2\u30eb\u30d0\u30e9\u306f\u3001\u4e00\u822c\u7684\u306b\u4f1a\u3046\u3053\u3068\u304c\u3067\u304d\u306a\u3044\u3044\u304f\u3064\u304b\u306e\u8ffd\u52a0\u7279\u6027\u3092\u6301\u3064\u901a\u52e4\u30a2\u30eb\u30df\u30cb\u30a6\u30e0\u3067\u3059\u3002 \u30e6\u30cb\u30bf\u30ea\u30a2\u30f3\u30fb\u30a2\u30eb\u30d0\u30e9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e00 \u30e6\u30cb\u30c6\u30fc\u30eb \u4ee3\u6570\u306f\u3001\u4e57\u7b97\u306e\u4e2d\u6027\u8981\u7d20\u3092\u6301\u3064\u4ee3\u6570\u3067\u3042\u308a\u3001\u9078\u629e\u3055\u308c\u3066\u3044\u307e\u3059\uff08\u7d71\u884c\u30ea\u30f3\u30b0\u3092\u53c2\u7167\uff09\u3002\u4f8b\uff1a \u5358\u4e00\u306e\u8981\u7d20\u3068\u3057\u3066\u30e6\u30cb\u30c3\u30c8\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u4f34\u3046\u7d50\u5a5a\u5f0f\u7d50\u5408\u3002 \u5358\u4e00\u306e\u30d5\u30a3\u30af\u30b7\u30e7\u30f3\u3068\u3057\u3066\u30a2\u30a4\u30c7\u30f3\u30c6\u30a3\u30c6\u30a3\u3092\u6301\u3064\u30d9\u30af\u30bf\u30fc\u30e1\u30a4\u30c8\u30c9\u30e2\u30eb\u30d5\u30a3\u30a2\u306e\u4ee3\u6570\u3002 \u6a5f\u80fd\u306f\u3001\u767a\u751f\u7387\u4ee3\u6570\u306e\u95a2\u6570\u3067\u3059 d \uff08 a \u3001 b \uff09\uff09 \uff1a= {1falls\u00a0a=b,0sonst.{displaystyle delta\uff08a\u3001b\uff09\uff1a= {begin {cases} 1quad\uff06{mbox {falls}} a = b\u3001\\ 0\uff06{mbox {sonst\u3002}} end {cases}}}}}} \u3059\u3079\u3066\u306e\u30b0\u30eb\u30fc\u30d7\u4ee3\u6570\u306f\u7d71\u4e00\u8005\u3067\u3059\u3002\u30b0\u30eb\u30fc\u30d7\u306e\u8981\u7d20\u306f\u3001\u4ee3\u6570\u306e\u8981\u7d20\u3067\u3082\u3042\u308a\u307e\u3059\u3002 \u4e00\u5b9a\u306e\u591a\u9805\u5f0f1\u306f\u3001\u591a\u9805\u5f0f\u306e\u8981\u7d20\u3067\u3059\u3002 \u4f53 k \u4ee3\u6570\u306e\u4e57\u7b97\u3068\u3057\u3066\u306e\u8eab\u4f53\u4e57\u7b97\u306b\u3088\u308a\u3001 k {displaystyle k}  – \u4ee3\u66ff\u3001\u5408\u6d41\u3001\u5358\u4f4d\u4e3b\u7fa9\u8005\u3002 \u3053\u308c\u304c\u305d\u308c\u305e\u308c\u306e\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u304b\u3089\u660e\u3089\u304b\u3067\u3042\u308b\u5834\u5408\u3001\u30d7\u30ed\u30d1\u30c6\u30a3\u306f\u4e00\u822c\u306b\u300c\u9023\u60f3\u300d\u3001\u300c\u901a\u52e4\u300d\u3001\u304a\u3088\u3073\u300c\u5358\u4f4d\u300d\u306b\u660e\u793a\u7684\u306b\u8a00\u53ca\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002\u4ee3\u6570\u306b\u8981\u7d20\u304c\u306a\u3044\u5834\u5408\u306f\u3001\u7de8\u96c6\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5404\u4ee3\u6570\u306f\u56e3\u4f53\u306b\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 \u95a2\u9023\u3057\u3066\u3044\u306a\u3044\u30a2\u30eb\u30d0\u30e9 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u4e00\u90e8\u306e\u8457\u8005\u306f1\u3064\u3092\u793a\u3057\u3066\u3044\u307e\u3059 k {displaystyle k}  – \u9280\u884cals \u975e\u5171\u540c \u9023\u60f3\u6cd5\u304c\u5fc5\u8981\u306a\u3044\u5834\u5408\u3002 [3] \uff08\u305f\u3060\u3057\u3001\u3053\u306e\u6982\u5ff5\u5f62\u6210\u306f\u3001\u7279\u306b\u3059\u3079\u3066\u306e\u9023\u60f3\u4ee3\u6570\u3082\u975e\u5171\u540c\u7684\u3067\u3042\u308b\u3068\u3044\u3046\u3084\u3084\u6df7\u4e71\u3057\u305f\u7d50\u679c\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002\uff09\u5fc5\u305a\u3057\u3082\u95a2\u9023\u3057\u3066\u3044\u306a\u3044\u30a2\u30eb\u30d0\u30e9\u306e\u3044\u304f\u3064\u304b\u306e\u4f8b\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 \u90e8\u9580\u306e\u30b5\u30eb\u30d6\u30e9\u306f\u3001\u300c\u5206\u5272\u300d\u3067\u304d\u308b\u4ee3\u6570\u3067\u3059\u3002 H.\u3059\u3079\u3066\u306e\u65b9\u7a0b\u5f0f\u3067 a \u30d0\u30c4 = b {displaystyle ax = b} \u3068 \u3068 a = b {displaystyle ya = b} \u305f\u3081\u306b a \u2260 0 {displaystyle aneq 0} \u5e38\u306b\u660e\u3089\u304b\u306b\u89e3\u6c7a\u53ef\u80fd\u3067\u3059\u3002\u90e8\u9580\u306e\u30b5\u30eb\u30d6\u30e9\u306f\u3001\u901a\u52e4\u3067\u3082\u9023\u60f3\u7684\u3067\u3082\u3001\u7d71\u884c\u7684\u3067\u3082\u306a\u3044\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 \u4ee3\u66ff\u4f53 o {displaystyle mathbb {o}} \u30b1\u30a4\u30ea\u30fc\u30fb\u30aa\u30af\u30bf\u30d9\u30f3\u306f\u30018\u6b21\u5143\u306e\u30e6\u30cb\u30bf\u30ea\u30a2\u30f3\u306e\u672c\u7269\u306e\u4ee3\u6570\u3067\u3042\u308a\u3001\u9023\u60f3\u4ee3\u6570 h {displaystyle mathbb {h}} \u30cf\u30df\u30eb\u30c8\u30f3\u306e\u56db\u5143\u6570\u306f\u672c\u5f53\u306b\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002 Lie-algebra\u306f\u4ee3\u6570\u3067\u3042\u308a\u3001\u6b21\u306e2\u3064\u306e\u6761\u4ef6\u304c\u9069\u7528\u3055\u308c\u307e\u3059\uff08Loy-Albangen\u3067\u306f\u3001\u901a\u5e38\u3001\u88fd\u54c1\u306f\u3068\u3057\u3066\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002 [ \u30d0\u30c4 \u3001 \u3068 ] {displaystyle [x\u3001y]} \u66f8\u304b\u308c\u305f\uff09\uff1a [x,x]=0{displayStyle [x\u3001x] = 0} [x,[y,z]]+[y,[z,x]]+[z,[x,y]]=0{displaystyle [x\u3001[y\u3001z]]+[y\u3001[z\u3001x]]+[z\u3001[x\u3001y] = 0} \uff08\u30e4\u30b3\u30d3\u306e\u30a2\u30a4\u30c7\u30f3\u30c6\u30a3\u30c6\u30a3\uff09 \u672c\u5f53\u306e\u30d9\u30af\u30bf\u30fc\u30e9\u30a6\u30e0 R3{displaystyle mathbb {r} ^{3}} \u30af\u30ed\u30b9\u88fd\u54c1\u3067\u3002\u3053\u306e\u672c\u5f53\u306e\u4ee3\u6570\u306f\u3001\u7279\u306b\u5618\u4ee3\u6570\u3067\u3059\u3002 \u30d0\u30ea\u30c3\u30af\u4ee3\u6570\u306f\u4ee3\u6570\u3067\u3059 a {displaystyle a} \u3001\u305d\u308c\u306f\u975e\u4e9b\u7d30\u306a\u30a2\u30eb\u30d0\u30eb\u540c\u6027\u611b\u3067\u3059 \u306e \uff1a a \u2192 k {displaystyle wcolon ato k} \u4e0e\u3048\u307e\u3059\u3002 \u9593\u306e\u6e96\u540c\u578b k {displaystyle k}  – \u30a2\u30ec\u30de\u30f3\u3001\u3064\u307e\u308a\u3001\u69cb\u9020\u7684\u306a\u753b\u50cf\u306f\u305d\u3046\u3067\u3059 k  – \u4e57\u6cd5\u7684\u306a\u7dda\u5f62\u30a4\u30e9\u30b9\u30c8\u3002\u30a2\u30eb\u30df\u30cb\u30a6\u30e0\u306e\u8981\u7d20\u306b1\u3064\u304c\u3042\u308b\u5834\u5408\u3001\u901a\u5e38\u306f\u4e92\u3044\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3055\u308c\u308b\u3053\u3068\u3082\u5fc5\u8981\u3067\u3059\u3002\u3064\u307e\u308a\u3001 \u30a4\u30e9\u30b9\u30c8 f \uff1a a \u2192 b {displaystyle fcolon arightarrow b} 2\u3064\u306e\u9593 k {displaystyle k}  – \u4ee5\u4e0b\u304c\u9069\u7528\u3055\u308c\u308b\u5834\u5408\u3001\u7db2\u819c\u306f\u540c\u6027\u611b\u3067\u3059\u3002 \u305d\u306e\u5f8c\u3001\u901a\u5e38\u306e\u6587\u304c\u9069\u7528\u3055\u308c\u307e\u3059\u3002\u540c\u6027\u611b\u306e\u30b3\u30a2\u306f\u3001\u307e\u3055\u306b2\u3064\u306e\u7406\u60f3\u3067\u3059\u3002\u306f f \uff1a a \u2192 b {displaystyle fcolon arightarrow b} \u540c\u7a2e\u6027\u3001\u30a2\u30ca\u30ed\u30b0\u306f\u540c\u578b\u3001\u3064\u307e\u308a\u8a98\u5c0e\u3055\u308c\u305f\u30a4\u30e9\u30b9\u30c8\u306b\u9069\u7528\u3055\u308c\u307e\u3059 f\u00af\uff1a a \/ k \u305d\u3046\u3067\u3059 r \uff08 f \uff09\uff09 \u2192 f \uff08 a \uff09\uff09 \u3001 a + k \u305d\u3046\u3067\u3059 r \uff08 f \uff09\uff09 \u21a6 f \uff08 a \uff09\uff09 {displaystyle {overline {f}} colon a\/mathrm {ker}\uff08f\uff09rightArrow f\uff08a\uff09,, a+mathrm {ker}\uff08f\uff09mapsto f\uff08a\uff09} \u660e\u78ba\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u304a\u308a\u3001\u30a2\u30eb\u30d0\u30ea\u30bd\u30e2\u30eb\u30d5\u30a3\u30ba\u30e0\u3067\u3059 a \/ k \u305d\u3046\u3067\u3059 r \uff08 f \uff09\uff09 \u2245 f \uff08 a \uff09\uff09 {displaystyle a\/mathrm {ker}\uff08f\uff09cong f\uff08a\uff09} \u3001\u3064\u307e\u308a\u3001\u751f\u7269\u306e\u30a2\u30eb\u30d0\u30eb\u540c\u6027\u75c7\u3067\u3042\u308b\u53cd\u8ee2\u753b\u50cf\u306f\u3001\u81ea\u52d5\u7684\u306b\u30a2\u30eb\u30d0\u30eb\u306e\u540c\u6027\u611b\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u901a\u5e38\u306e\u8a3c\u62e0\u304c\u305d\u308c\u3089\u3092\u540c\u97f3\u578b\u306b\u8d77\u56e0\u3059\u308b\u305f\u3081\u3001\u3053\u308c\u306f\u30a2\u30eb\u30d0\u30e9\u306b\u7570\u578b\u30ec\u30fc\u30c8\u306b\u8ee2\u9001\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 \u2191  z\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 B.\u30c7\u30a3\u30af\u30bd\u30f3\uff081905\uff09\u3001 https:\/\/mathshistory.st-andrews.ac.uk\/extras\/dickson_lineear_algebras\/  \u2191  \u672c\u5f53\u306e\u4ee3\u6570 \u3002 In\uff1aGuido Walz\uff08\u7de8\uff09\uff1a \u6570\u5b66\u306e\u8f9e\u66f8 \u3002\u7b2c1\u7248\u3002 Spectrum Akademischer Verlag\u3001Mannheim\/Heidelberg 2000\u3001ISBN 978-3-8274-0439-8\u3002   \u2191  z\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002 B. R. Lidl\u3068J. Wiesenbauer\u3001 \u30ea\u30f3\u30b0\u7406\u8ad6\u3068\u305d\u306e\u5fdc\u7528 \u3001Wiesbaden 1980\u3001ISBN 3-400-00371-9       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@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\/4664#breadcrumbitem","name":"\u30dc\u30c7\u30a3\u4e0a\u306e\u4ee3\u6570 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2"}}]}]