{"id":682,"date":"2013-03-12T21:51:37","date_gmt":"2013-03-12T12:51:37","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=682"},"modified":"2021-09-16T07:05:01","modified_gmt":"2021-09-15T22:05:01","slug":"ngr200701","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ngr200701\/","title":{"rendered":"\u540d\u53e4\u5c4b\u5927\u7406\u7cfb2007\uff1a\u7b2c1\u554f"},"content":{"rendered":"
\n

\\(2\\) \u884c \\(2\\) \u5217\u306e\u884c\u5217 \\(\\left( \\begin{array}{cc} a & b \\\\ c & d \\end{array} \\right)\\) \u3092\u8003\u3048\u308b.\r\n\\(a , b , d\\) \u304c\u5b9f\u6570\u3067 \\(c = 0\\) \u3067\u3042\u308b\u884c\u5217 \\(\\left( \\begin{array}{cc} a & b \\\\ 0 & d \\end{array} \\right)\\) \u3092\u4e0a\u4e09\u89d2\u884c\u5217\u3068\u3044\u3046. \u307e\u305f, \\(E = \\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & 1 \\end{array} \\right)\\) \u3068\u304a\u304f.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(A^2 = E\\) \u3092\u307f\u305f\u3059\u4e0a\u4e09\u89d2\u884c\u5217 \\(A\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(A^3 = E\\) \u3092\u307f\u305f\u3059\u4e0a\u4e09\u89d2\u884c\u5217 \\(A\\) \u3092\u3059\u3079\u3066\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u4e0a\u4e09\u89d2\u884c\u5217 \\(A\\) \u304c \\(A^4 = E\\) \u3092\u307f\u305f\u3059\u3068\u304d, \\(A^2 = E\\) \u3068\u306a\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

    (1)<\/strong><\/p>\r\n

    \\[\\begin{align}\r\nA^2 & = \\left( \\begin{array}{cc} a & b \\\\ 0 & d \\end{array} \\right) \\left( \\begin{array}{cc} a & b \\\\ 0 & d \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{cc} a^2 & b(a+d) \\\\ 0 & d^2 \\end{array} \\right) \\ .\r\n\\end{align}\\]\r\n\\(A^2 = E\\) \u306a\u306e\u3067, \u6210\u5206\u3092\u6bd4\u8f03\u3059\u308c\u3070\r\n\\[\r\n\\left\\{ \\begin{array}{l} a^2 = d^2 = 1 \\quad ... [1] \\\\ b(a+d) = 0 \\quad ... [2] \\end{array} \\right. \\ .\r\n\\]\r\n[2] \u3088\u308a\r\n\\[\r\nb = 0 \\ \\text{\u307e\u305f\u306f} \\ a+d = 0 \\ .\r\n\\]\r\n

      \r\n

    1. 1*<\/strong>\u3000\\(b = 0\\) \u306e\u3068\u304d
      \r\n[1] \u3088\u308a\r\n\\[\r\na = \\pm 1 , \\ d = \\pm 1 \\ .\r\n\\]<\/li>\r\n

    2. 2*<\/strong>\u3000\\(a+d = 0\\) \u306e\u3068\u304d
      \r\n[1] \u3088\u308a\r\n\\[\r\n(a,d) = ( \\pm 1 , \\mp 1 ) \\quad ( \\text{\u8907\u53f7\u540c\u9806} ) \\ .\r\n\\]<\/li>\r\n<\/ol>\r\n

      \u4ee5\u4e0a\u3088\u308a, \u6c42\u3081\u308b \\(A\\) \u306f\r\n\\[\\begin{align}\r\nA = & \\underline{\\left( \\begin{array}{cc} \\pm 1 & 0 \\\\ 0 & \\pm 1 \\end{array} \\right) \\quad ( \\text{\u8907\u53f7\u4efb\u610f} ) , }\\\\\r\n& \\underline{\\left( \\begin{array}{cc} \\pm 1 & k \\\\ 0 & \\mp 1 \\end{array} \\right) \\quad ( \\text{\u8907\u53f7\u540c\u9806} , \\ k \\text{\u306f\u4efb\u610f\u306e\u5b9f\u6570} )} \\ .\r\n\\end{align}\\]\r\n

      (2)<\/strong><\/p>\r\n

      \\[\\begin{align}\r\nA^3 & = \\left( \\begin{array}{cc} a^2 & b(a+d) \\\\ 0 & d^2 \\end{array} \\right) \\left( \\begin{array}{cc} a & b \\\\ 0 & d \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{cc} a^3 & b( a^2+ad+d^2 ) \\\\ 0 & d^3 \\end{array} \\right) \\ .\r\n\\end{align}\\]\r\n\\(A^3 = E\\) \u306a\u306e\u3067, \u6210\u5206\u3092\u6bd4\u8f03\u3059\u308c\u3070\r\n\\[\r\n\\left\\{ \\begin{array}{l} a^3 = d^3 = 1 \\quad ... [3] \\\\ b(a^2+ad+d^2) = 0 \\quad ... [4] \\end{array} \\right. \\ .\r\n\\]\r\n\\(a ,d\\) \u306f\u5b9f\u6570\u306a\u306e\u3067, [3] \u3088\u308a\r\n\\[\r\na=d=1 \\ .\r\n\\]\r\n[4] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\\begin{align}\r\n3b & = 0 \\\\\r\n\\text{\u2234} \\quad b & = 0 \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\u6c42\u3081\u308b \\(A\\) \u306f\r\n\\[\r\nA = \\underline{\\left( \\begin{array}{cc} 1 & 0 \\\\ 0 & 1 \\end{array} \\right)} \\ .\r\n\\]\r\n

      (3)<\/strong><\/p>\r\n

      \\[\\begin{align}\r\nA^4 & = \\left( \\begin{array}{cc} a^3 & b( a^2+ad+d^2 ) \\\\ 0 & d^3 \\end{array} \\right) \\left( \\begin{array}{cc} a & b \\\\ 0 & d \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{cc} a^4 & b( a^3+a^2d+ad^2+d^3 ) \\\\ 0 & d^4 \\end{array} \\right) \\ .\r\n\\end{align}\\]\r\n\\(A^4 = E\\) \u306a\u306e\u3067, \u6210\u5206\u3092\u6bd4\u8f03\u3059\u308c\u3070\r\n\\[\r\n\\left\\{ \\begin{array}{l} a^4 = d^4 = 1 \\quad ... [5] \\\\ b( a^3+a^2d+ad^2+d^3 ) = 0 \\quad ...[6] \\end{array} \\right. \\ .\r\n\\]\r\n\\(a ,d\\) \u306f\u5b9f\u6570\u306a\u306e\u3067, [5] \u3088\u308a\r\n\\[\r\na^2 = d^2 = 1 \\quad ... [7] \\ .\r\n\\]\r\n[7] \u3092 [6] \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n\\[\\begin{align}\r\nb ( a+d+a+d ) & = 0 \\\\\r\n\\text{\u2234} \\quad b(a+d) & = 0 \\quad ... [8] \\ .\r\n\\end{align}\\]\r\n[7] \u304b\u3064 [8] \u306f, [1] \u304b\u3064 [2] \u3068\u7b49\u3057\u3044.
      \r\n\u3088\u3063\u3066, \\(A^4 = E\\) \u3092\u307f\u305f\u3059 \\(A\\) \u306f, (1)<\/strong> \u306e\u7d50\u679c\u3068\u7b49\u3057\u304f, \u3059\u306a\u308f\u3061 \\(A^2 = E\\) \u3092\u307f\u305f\u3059.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(2\\) \u884c \\(2\\) \u5217\u306e\u884c\u5217 \\(\\left( \\begin{array}{cc} a & b \\\\ c & d \\end{array} \\right)\\) \u3092\u8003\u3048\u308b. \\(a , b , d\\) \u304c\u5b9f\u6570\u3067 \\( … \u7d9a\u304d\u3092\u8aad\u3080 →<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[97],"tags":[143,109],"class_list":["post-682","post","type-post","status-publish","format-standard","hentry","category-nagoya_r_2007","tag-nagoya_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/682","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=682"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/682\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}