[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/117424#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/117424","headline":"\u5341\u516d\u5143\u6570 – Wikipedia","name":"\u5341\u516d\u5143\u6570 – Wikipedia","description":"\u62bd\u8c61\u4ee3\u6570\u5b66\u306b\u304a\u3051\u308b\u5341\u516d\u5143\u6570\uff08\u3058\u3085\u3046\u308d\u304f\u3052\u3093\u3059\u3046\u3001\u82f1: sedenion\uff09\u306f\u3001\u5168\u4f53\u3068\u3057\u3066\u5b9f\u6570\u4f53 R \u4e0a16\u6b21\u5143\u306e\uff08\u53cc\u7dda\u578b\u306a\u4e57\u6cd5\u3092\u6301\u3064\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u3044\u3046\u610f\u5473\u3067\u306e\uff09\u975e\u7d50\u5408\u7684\u5206\u914d\u591a\u5143\u74b0\u3092\u6210\u3059\u4ee3\u6570\u7684\u306a\u5bfe\u8c61\u3067\u3001\u305d\u306e\u5168\u4f53\u306f\u3057\u3070\u3057\u3070 S \u3067\u8868\u3055\u308c\u308b\u3002\u516b\u5143\u6570\u306b\u30b1\u30fc\u30ea\u30fc\uff1d\u30c7\u30a3\u30af\u30bd\u30f3\u306e\u69cb\u6210\u6cd5\u3092\u4f7f\u3063\u3066\u5f97\u3089\u308c\u308b\u5bfe\u5408\u7684\u4e8c\u6b21\u4ee3\u6570\u3067\u3042\u308b\u3002 \u300c\u5341\u516d\u5143\u6570\u300d\u3068\u3044\u3046\u7528\u8a9e\u306f\u3001\u4ed6\u306e\u5341\u516d\u6b21\u5143\u4ee3\u6570\u69cb\u9020\u3001\u4f8b\u3048\u3070\u56db\u5143\u6570\u306e\u8907\u88fd\u4e8c\u3064\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\u3084\u5b9f\u6570\u4f53\u4e0a\u306e\u56db\u6b21\u6b63\u65b9\u884c\u5217\u74b0\u306a\u3069\u306b\u5bfe\u3057\u3066\u3082\u7528\u3044\u3089\u308c\u3001Smith (1995) \u3067\u8abf\u3079\u3089\u308c\u3066\u3044\u308b\u3002 \u30b1\u30fc\u30ea\u30fc\u306e\u516b\u5143\u6570\u3068\u540c\u69d8\u306b\u5341\u516d\u5143\u6570\u306e\u4e57\u6cd5\u306f\u53ef\u63db\u3067\u3082\u7d50\u5408\u7684\u3067\u3082\u306a\u3044\u3002\u305d\u3057\u3066\u3001\u30b1\u30fc\u30ea\u30fc\u306e\u516b\u5143\u6570\u74b0 O \u3068\u660e\u78ba\u306b\u9055\u3046\u3053\u3068\u306b\u3001\u5341\u516d\u5143\u6570\u306e\u5168\u4f53 S \u306f\u4ea4\u4ee3\u4ee3\u6570\u306b\u3082\u306a\u3089\u306a\u3044\u3002\u5341\u516d\u5143\u6570\u306b\u3064\u3044\u3066\u3044\u3048\u308b\u3053\u3068\u306f\u51aa\u7d50\u5408\u6027\uff08\u82f1\u8a9e\u7248\uff09\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u308c\u306f S \u306e\u5143 x \u306b\u5bfe\u3057\u3066\u3001\u51aa xn \u306f\u77db\u76fe\u306a\u304f\u5b9a\u7fa9\u53ef\u80fd\u3067\u3001\u305d\u308c\u3089\u304c\u67d4\u8edf\uff08\u82f1\u8a9e\u7248\uff09\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002","datePublished":"2022-03-18","dateModified":"2022-03-18","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/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:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/25fe838c098efe486d67fc2861327477f1df6ad8","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/25fe838c098efe486d67fc2861327477f1df6ad8","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/117424","about":["Wiki"],"wordCount":5338,"articleBody":"\u62bd\u8c61\u4ee3\u6570\u5b66\u306b\u304a\u3051\u308b\u5341\u516d\u5143\u6570\uff08\u3058\u3085\u3046\u308d\u304f\u3052\u3093\u3059\u3046\u3001\u82f1: sedenion\uff09\u306f\u3001\u5168\u4f53\u3068\u3057\u3066\u5b9f\u6570\u4f53 R \u4e0a16\u6b21\u5143\u306e\uff08\u53cc\u7dda\u578b\u306a\u4e57\u6cd5\u3092\u6301\u3064\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u3044\u3046\u610f\u5473\u3067\u306e\uff09\u975e\u7d50\u5408\u7684\u5206\u914d\u591a\u5143\u74b0\u3092\u6210\u3059\u4ee3\u6570\u7684\u306a\u5bfe\u8c61\u3067\u3001\u305d\u306e\u5168\u4f53\u306f\u3057\u3070\u3057\u3070 S \u3067\u8868\u3055\u308c\u308b\u3002\u516b\u5143\u6570\u306b\u30b1\u30fc\u30ea\u30fc\uff1d\u30c7\u30a3\u30af\u30bd\u30f3\u306e\u69cb\u6210\u6cd5\u3092\u4f7f\u3063\u3066\u5f97\u3089\u308c\u308b\u5bfe\u5408\u7684\u4e8c\u6b21\u4ee3\u6570\u3067\u3042\u308b\u3002  \u300c\u5341\u516d\u5143\u6570\u300d\u3068\u3044\u3046\u7528\u8a9e\u306f\u3001\u4ed6\u306e\u5341\u516d\u6b21\u5143\u4ee3\u6570\u69cb\u9020\u3001\u4f8b\u3048\u3070\u56db\u5143\u6570\u306e\u8907\u88fd\u4e8c\u3064\u306e\u30c6\u30f3\u30bd\u30eb\u7a4d\u3084\u5b9f\u6570\u4f53\u4e0a\u306e\u56db\u6b21\u6b63\u65b9\u884c\u5217\u74b0\u306a\u3069\u306b\u5bfe\u3057\u3066\u3082\u7528\u3044\u3089\u308c\u3001Smith (1995) \u3067\u8abf\u3079\u3089\u308c\u3066\u3044\u308b\u3002\u30b1\u30fc\u30ea\u30fc\u306e\u516b\u5143\u6570\u3068\u540c\u69d8\u306b\u5341\u516d\u5143\u6570\u306e\u4e57\u6cd5\u306f\u53ef\u63db\u3067\u3082\u7d50\u5408\u7684\u3067\u3082\u306a\u3044\u3002\u305d\u3057\u3066\u3001\u30b1\u30fc\u30ea\u30fc\u306e\u516b\u5143\u6570\u74b0 O \u3068\u660e\u78ba\u306b\u9055\u3046\u3053\u3068\u306b\u3001\u5341\u516d\u5143\u6570\u306e\u5168\u4f53 S \u306f\u4ea4\u4ee3\u4ee3\u6570\u306b\u3082\u306a\u3089\u306a\u3044\u3002\u5341\u516d\u5143\u6570\u306b\u3064\u3044\u3066\u3044\u3048\u308b\u3053\u3068\u306f\u51aa\u7d50\u5408\u6027\uff08\u82f1\u8a9e\u7248\uff09\u3092\u6301\u3063\u3066\u3044\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u308c\u306f S \u306e\u5143 x \u306b\u5bfe\u3057\u3066\u3001\u51aa xn \u306f\u77db\u76fe\u306a\u304f\u5b9a\u7fa9\u53ef\u80fd\u3067\u3001\u305d\u308c\u3089\u304c\u67d4\u8edf\uff08\u82f1\u8a9e\u7248\uff09\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u4efb\u610f\u306e\u5341\u516d\u5143\u6570\u306f\u3001R-\u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3068\u3057\u3066\u306e S \u306e\u57fa\u5e95\u3092\u6210\u305916\u500b\u306e\u5358\u4f4d\u5341\u516d\u5143\u6570 e0 = 1, e1, e2, e3, \u2026, e15 \u306e\u5b9f\u4fc2\u6570\u7dda\u578b\u7d50\u5408\u306b\u306a\u3063\u3066\u3044\u308b\u3002  \u5341\u516d\u5143\u6570\u306f\u4e57\u6cd5\u306b\u95a2\u3059\u308b\u5358\u4f4d\u5143\u3092\u6301\u3061\u3001\u591a\u304f\u306e\u5143\u304c\u305d\u306e\u9006\u5143\u3092\u6301\u3064\u304c\u3001\u591a\u5143\u4f53\u3068\u306f\u306a\u3089\u306a\u3044\u3002\u3053\u308c\u306f\u96f6\u56e0\u5b50\u306e\u5b58\u5728\u306b\u3088\u308b\u3002\u3064\u307e\u308a\u3001\u305d\u308c\u81ea\u4f53\u306f\u96f6\u3067\u306f\u306a\u3044\u304c\u639b\u3051\u308b\u3068\u96f6\u306b\u306a\u308b\u3088\u3046\u306a\u5341\u516d\u5143\u6570\u306e\u7d44\u304c\u3042\u308b\u306e\u3060\u304c\u3001\u7c21\u5358\u306a\u4f8b\u3068\u3057\u3066\u306f (e3 + e10) \u00d7 (e6 \u2212 e15) \u306a\u3069\u3092\u6319\u3052\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5341\u516d\u5143\u6570\u304b\u3089\u30b1\u30fc\u30ea\u30fc\uff1d\u30c7\u30a3\u30af\u30bd\u30f3\u306e\u69cb\u6210\u6cd5\u3092\u5143\u306b\u3057\u3066\u4f5c\u3089\u308c\u308b\u3069\u306e\u8d85\u8907\u7d20\u6570\u7cfb\u3082\u96f6\u56e0\u5b50\u3092\u542b\u3080\u3002\u5358\u4f4d\u5341\u516d\u5143\u6570\u306e\u4e57\u7a4d\u8868\u306f\u6b21\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3042\u308b\u3002\u57fa\u5e95\u306e\u4e57\u7a4d\u8868\u00d71e1e2e3e4e5e6e7e8e9e10e11e12e13e14e1511e1e2e3e4e5e6e7e8e9e10e11e12e13e14e15e1e1\u22121e3\u2212e2e5\u2212e4\u2212e7e6e9\u2212e8\u2212e11e10\u2212e13e12e15\u2212e14e2e2\u2212e3\u22121e1e6e7\u2212e4\u2212e5e10e11\u2212e8\u2212e9\u2212e14\u2212e15e12e13e3e3e2\u2212e1\u22121e7\u2212e6e5\u2212e4e11\u2212e10e9\u2212e8\u2212e15e14\u2212e13e12e4e4\u2212e5\u2212e6\u2212e7\u22121e1e2e3e12e13e14e15\u2212e8\u2212e9\u2212e10\u2212e11e5e5e4\u2212e7e6\u2212e1\u22121\u2212e3e2e13\u2212e12e15\u2212e14e9\u2212e8e11\u2212e10e6e6e7e4\u2212e5\u2212e2e3\u22121\u2212e1e14\u2212e15\u2212e12e13e10\u2212e11\u2212e8e9e7e7\u2212e6e5e4\u2212e3\u2212e2e1\u22121e15e14\u2212e13\u2212e12e11e10\u2212e9\u2212e8e8e8\u2212e9\u2212e10\u2212e11\u2212e12\u2212e13\u2212e14\u2212e15\u22121e1e2e3e4e5e6e7e9e9e8\u2212e11e10\u2212e13e12e15\u2212e14\u2212e1\u22121\u2212e3e2\u2212e5e4e7\u2212e6e10e10e11e8\u2212e9\u2212e14\u2212e15e12e13\u2212e2e3\u22121\u2212e1\u2212e6\u2212e7e4e5e11e11\u2212e10e9e8\u2212e15e14\u2212e13e12\u2212e3\u2212e2e1\u22121\u2212e7e6\u2212e5e4e12e12e13e14e15e8\u2212e9\u2212e10\u2212e11\u2212e4e5e6e7\u22121\u2212e1\u2212e2\u2212e3e13e13\u2212e12e15\u2212e14e9e8e11\u2212e10\u2212e5\u2212e4e7\u2212e6e1\u22121e3\u2212e2e14e14\u2212e15\u2212e12e13e10\u2212e11e8e9\u2212e6\u2212e7\u2212e4e5e2\u2212e3\u22121e1e15e15e14\u2212e13\u2212e12e11e10\u2212e9e8\u2212e7e6\u2212e5\u2212e4e3e2\u2212e1\u22121\u4e00\u822c\u306e\u5341\u516d\u5143\u6570\u306e\u7a4d\u306f\u57fa\u5e95\u306b\u304a\u3051\u308b\u4e57\u6cd5\u3092\uff08\u5206\u914d\u6cd5\u5247\u304c\u6210\u308a\u7acb\u3064\u3088\u3046\u306b\uff09\u7dda\u578b\u306b\u62e1\u5f35\u3059\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u3002\u5341\u516d\u5143\u6570\u306e\u5168\u4f53 S \u306f\u5171\u8edb\u5143\u3092\u3068\u308b\u4e3b\u5bfe\u5408  x=\u2211i=015xiei\u21a6x\u2217:=x01\u2212\u2211i=115xiei{displaystyle x=sum _{i=0}^{15}x_{i}e_{i}mapsto x^{*}:=x_{0}1-sum _{i=1}^{15}x_{i}e_{i}}\u306b\u3088\u3063\u3066\u30ce\u30eb\u30e0N(x):=xx\u2217=\u2211i=015xi2(or\u00a0\u2016x\u2016:=xx\u2217){displaystyle N(x):=xx^{*}=sum _{i=0}^{15}x_{i}^{2}quad ({text{or }}|x|:={sqrt {xx^{*}}})}\u306e\u5b9a\u307e\u308b\u4e8c\u6b21\u4ee3\u6570 (S, N) \u3067\u3042\u308b\u304c\u3001\u3053\u308c\u306f\u30ce\u30eb\u30e0\u304c\u4e57\u6cd5\u7684\u3067\u306a\u3044\u3002Moreno (1998) \u306f\u30ce\u30eb\u30e0 1 \u306e\u5341\u516d\u5143\u6570\u304b\u3089\u306a\u308b\u639b\u3051\u3066 0 \u3068\u306a\u308b\u5bfe\u306e\u5168\u4f53\u304c\u3001\u4f8b\u5916\u578b\u30ea\u30fc\u7fa4 G2 \u306e\u30b3\u30f3\u30d1\u30af\u30c8\u578b\u306b\u540c\u578b\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u305f\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]Imaeda, K.; Imaeda, M. (2000), \u201cSedenions: algebra and analysis\u201d, Applied mathematics and computation 115 (2):  77\u201388, doi:10.1016\/S0096-3003(99)00140-X, MR1786945\u00a0Kinyon, M.K., Phillips, J.D., Vojt\u011bchovsk\u00fd, P.: C-loops: Extensions and constructions, Journal of Algebra and its Applications 6  (2007), no. 1, 1\u201320. [1]Kivunge, Benard M. and Smith, Jonathan D. H: “Subloops of sedenions“, Comment.Math.Univ.Carolinae 45,2 (2004)295\u2013302.Moreno, Guillermo (1998), \u201cThe zero divisors of the Cayley-Dickson algebras over the real numbers\u201d, Sociedad Matem\u00e1tica Mexicana. Bolet\u00ed n. Tercera Serie 4 (1):  13\u201328, arXiv:q-alg\/9710013, MR1625585\u00a0Smith, Jonathan D. H. (1995), \u201cA left loop on the 15-sphere\u201d, Journal of Algebra 176 (1):  128\u2013138, doi:10.1006\/jabr.1995.1237, MR1345298\u00a0"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki10\/archives\/117424#breadcrumbitem","name":"\u5341\u516d\u5143\u6570 – Wikipedia"}}]}]