{"id":602,"date":"2013-02-02T07:49:14","date_gmt":"2013-02-01T22:49:14","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=602"},"modified":"2021-03-18T15:23:41","modified_gmt":"2021-03-18T06:23:41","slug":"tkr200704","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tkr200704\/","title":{"rendered":"\u6771\u5927\u7406\u7cfb2007\uff1a\u7b2c4\u554f"},"content":{"rendered":"
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\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057, \\(2\\) \u6b21\u306e\u6b63\u65b9\u884c\u5217 \\(A , P , Q\\) \u304c,\r\n\\(5\\) \u3064\u306e\u6761\u4ef6 \\(A = a P +(a+1) Q\\) , \\(P^2 = P\\) , \\(Q^2 = Q\\) , \\(PQ = O\\) , \\(QP = O\\) \u3092\u307f\u305f\u3059\u3068\u3059\u308b.\r\n\u305f\u3060\u3057, \\(O = \\left( \\begin{array}{cc} 0 & 0 \\\\ 0 & 0 \\end{array} \\right)\\) \u3067\u3042\u308b.\r\n\u3053\u306e\u3068\u304d, \\((P+Q) A = A\\) \u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(a\\) \u306f\u6b63\u306e\u6570\u3068\u3057\u3066, \u884c\u5217 \\(A = \\left( \\begin{array}{cc} a & 0 \\\\ 1 & a+1 \\end{array} \\right)\\) \u3092\u8003\u3048\u308b.\r\n\u3053\u306e \\(A\\) \u306b\u5bfe\u3057, (1)<\/strong> \u306e \\(5\\) \u3064\u306e\u6761\u4ef6\u3092\u3059\u3079\u3066\u307f\u305f\u3059\u884c\u5217 \\(P , Q\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(n\\) \u3092 \\(2\\) \u4ee5\u4e0a\u306e\u6574\u6570\u3068\u3057, \\(2 \\leqq k \\leqq n\\) \u3092\u307f\u305f\u3059\u6574\u6570 \\(k\\) \u306b\u5bfe\u3057\u3066 \\(A _ k = \\left( \\begin{array}{cc} k & 0 \\\\ 1 & k+1 \\end{array} \\right)\\) \u3068\u304a\u304f.\r\n\u884c\u5217\u306e\u7a4d \\(A _ {n} A _ {n-1} A _ {n-2} \\cdots A _ {2}\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u6761\u4ef6\u3092\u7528\u3044\u308c\u3070\r\n\\[\\begin{align}\r\n(P+Q) A & = (P+Q) \\left\\{ aP +(1-a)Q \\right\\} \\\\\r\n& = a P^2 +(1-a) Q^2 \\quad ( \\ \\text{\u2235} \\ PQ =QP =O \\ ) \\\\\r\n& = aP +(1-a)Q \\quad ( \\ \\text{\u2235} \\ P^2=P , \\ Q^2=Q \\ ) \\\\\r\n& = A\r\n\\end{align}\\]\r\n

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

    (1)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\\begin{align}\r\nP+Q & = E \\\\\r\n\\text{\u2234} \\quad Q & = E-P\r\n\\end{align}\\]\r\n\\(P = \\left( \\begin{array}{cc} p & q \\\\ r & s \\end{array} \\right)\\) \u3068\u304a\u3051\u3070\r\n\\[\r\nQ = \\left( \\begin{array}{cc} 1-p & -q \\\\ -r & 1-s \\end{array} \\right)\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\left( \\begin{array}{cc} a & 0 \\\\ 1 & a+1 \\end{array} \\right) & = \\left( \\begin{array}{cc} ap +(a+1)(1-p) & aq -(a+1)q \\\\ ar-(a+1)r & as+(a+1)(1-s) \\end{array} \\right) \\\\\r\n& = \\left( \\begin{array}{cc} a+1-p & -q \\\\ -r & a+1-s \\end{array} \\right)\r\n\\end{align}\\]\r\n\u5404\u6210\u5206\u3092\u6bd4\u8f03\u3059\u308c\u3070\r\n\\[\r\np=1 , \\ q=0 , \\ r =-1 , \\ s =0\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\nP =\\underline{\\left( \\begin{array}{cc} 1 & 0 \\\\ -1 & 0 \\end{array} \\right)} , \\ Q = \\underline{\\left( \\begin{array}{cc} 0 & 0 \\\\ 1 & 1 \\end{array} \\right)}\r\n\\]\r\n

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

    \\(A _ k = kP +(k+1)Q\\) \u3068\u304a\u3044\u3066\u639b\u3051\u5408\u308f\u305b\u308c\u3070\r\n\\[\\begin{align}\r\nA _ n \\cdots A _ 3 A _ 2 & = n \\cdots 3 \\cdot 2 P^{n-1} +(n+1) \\cdots 4 \\cdot 3 Q^{n-1} \\\\\r\n& = n! P +\\dfrac{(n+1) !}{2} Q \\\\\r\n& =\\left( \\begin{array}{cc} n ! & 0 \\\\ -n ! +\\dfrac{(n+1) !}{2} & \\dfrac{(n+1) !}{2} \\end{array} \\right) \\\\\r\n& =\\underline{\\left( \\begin{array}{cc} n ! & 0 \\\\ -\\dfrac{(n-1) n !}{2} & \\dfrac{(n+1) !}{2} \\end{array} \\right)} \\\\\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088. (1)\u3000\u5b9f\u6570 \\(a\\) \u306b\u5bfe\u3057, \\(2\\) \u6b21\u306e\u6b63\u65b9\u884c\u5217 \\(A , P , Q\\) \u304c, \\(5\\) \u3064\u306e\u6761\u4ef6 \\(A = a P +(a+1) Q\\) , \\(P^2 = P\\) , \\(Q … \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":[85],"tags":[139,109],"class_list":["post-602","post","type-post","status-publish","format-standard","hentry","category-tokyo_r_2007","tag-tokyo_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/602","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=602"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/602\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=602"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=602"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=602"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}