{"id":614,"date":"2013-02-11T11:44:23","date_gmt":"2013-02-11T02:44:23","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=614"},"modified":"2021-03-24T09:51:37","modified_gmt":"2021-03-24T00:51:37","slug":"kyr200705","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr200705\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb\u4e592007\uff1a\u7b2c5\u554f"},"content":{"rendered":"<hr \/>\n<p>\\(A\\) \u3092 \\(2\\) \u6b21\u306e\u6b63\u65b9\u884c\u5217\u3068\u3059\u308b. \u5217\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{x _ 0}\\) \u306b\u5bfe\u3057, \u5217\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{x _ 1} , \\overrightarrow{x _ 2} , \\cdots\\) \u3092\r\n\\[\r\n\\overrightarrow{x _ {n+1}} = A \\overrightarrow{x _ n} \\quad ( n = 0, 1, 2, \\cdots )\r\n\\]\r\n\u306b\u3088\u3063\u3066\u5b9a\u3081\u308b.\r\n\u3042\u308b\u96f6\u30d9\u30af\u30c8\u30eb\u3067\u306f\u306a\u3044 \\(\\overrightarrow{x _ 0}\\) \u306b\u3064\u3044\u3066, \\(3\\) \u4ee5\u4e0a\u306e\u81ea\u7136\u6570 \\(m\\) \u3067\u521d\u3081\u3066 \\(\\overrightarrow{x _ m}\\) \u304c \\(\\overrightarrow{x _ 0}\\) \u3068\u4e00\u81f4\u3059\u308b\u3068\u304d, \u884c\u5217 \\(A^m\\) \u306f\u5358\u4f4d\u884c\u5217\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p>\r\n<hr>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p>\u6761\u4ef6\u3088\u308a\r\n\\[\r\nA^m \\overrightarrow{x _ 0} = \\overrightarrow{x _ 0} \\quad ... [1]\r\n\\]\r\n[1] \u306e\u4e21\u8fba\u306b\u53f3\u304b\u3089 \\(A\\) \u3092\u304b\u3051\u308c\u3070\r\n\\[\\begin{align}\r\nA^{m+1} \\overrightarrow{x _ 0} & = A \\overrightarrow{x _ 0} \\\\\r\n\\text{\u2234} \\quad A^{m} \\overrightarrow{x _ 1} & = \\overrightarrow{x _ 1} \\quad ... [2]\r\n\\end{align}\\]\r\n\u3053\u306e\u3068\u304d, \\(\\overrightarrow{x _ 0} \\neq \\overrightarrow{x _ 1}\\)<\/p>\r\n<ol>\r\n<li><p><strong>1*<\/strong>\u3000\\(\\overrightarrow{x _ 1} = 0\\) \u306e\u3068\u304d<br \/>\r\n\\(n \\geqq 1\\) \u306b\u5bfe\u3057\u3066 \\(\\overrightarrow{x _ n} = 0\\) \u3068\u306a\u308a, \u4e0d\u9069.<\/p><\/li>\r\n<li><p><strong>2*<\/strong>\u3000\\(\\overrightarrow{x _ 1} = k \\overrightarrow{x _ 0} \\ ( k \\neq 1 )\\) \u306e\u3068\u304d\r\n\\[\\begin{align}\r\nA^m \\overrightarrow{x _ 0} & = k^m \\overrightarrow{x _ 0} = \\overrightarrow{x _ 0} \\quad ( \\ \\text{\u2235} \\ [1] \\ ) \\\\\r\n\\text{\u2234} \\quad & ( k^m -1 ) \\overrightarrow{x _ 0} = 0\r\n\\end{align}\\]\r\n\\(\\overrightarrow{x _ 0} \\neq 0\\) \u306a\u306e\u3067\r\n\\[\r\nk^m -1 = 0\r\n\\]\r\n\\(m \\geqq 3\\) \u306b\u6ce8\u610f\u3059\u308b\u3068\r\n<ul>\r\n<li>\\(m\\) \u304c\u5076\u6570\u306e\u3068\u304d<br \/>\r\n\\(k=-1\\) \u3092\u89e3\u306b\u3082\u3064\u304c \\(m=2\\) \u306e\u3068\u304d\u3082\u540c\u3058\u89e3\u3092\u3082\u3064\u305f\u3081, \\(\\overrightarrow{x _ 0} = \\overrightarrow{x _ 2}\\) \u3068\u306a\u308a\u4e0d\u9069.<\/li>\r\n<li>\\(m\\) \u304c\u5947\u6570\u306e\u3068\u304d\u306f, \u89e3\u306a\u3057.<\/li>\r\n<\/ul>\r\n\u306a\u306e\u3067, \u6761\u4ef6\u3092\u6e80\u305f\u3059 \\(k\\) \u306f\u5b58\u5728\u305b\u305a\u4e0d\u9069.<\/p><\/li>\r\n<li><strong>3*<\/strong>\u3000\\(\\overrightarrow{x _ 0} , \\overrightarrow{x _ 1}\\) \u304c \\(1\\) \u6b21\u72ec\u7acb\u3067\u3042\u308b\u3068\u304d<br \/>\r\n\u4efb\u610f\u306e\u5217\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{x}\\) \u304c \u5b9f\u6570 \\(p, q\\) \u3092\u7528\u3044\u3066\r\n\\[\r\n\\overrightarrow{x} = p \\overrightarrow{x _ 0} +q \\overrightarrow{x _ 1}\r\n\\]\r\n\u3068\u8868\u305b\u308b. [1] [2] \u3092\u7528\u3044\u308b\u3068\r\n\\[\\begin{align}\r\nA^m \\overrightarrow{x} & = p A^m \\overrightarrow{x _ 0} +q A^m \\overrightarrow{x _ 1} \\\\\r\n& = p \\overrightarrow{x _ 0} +q \\overrightarrow{x _ 1} = \\overrightarrow{x}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u3053\u306e\u3068\u304d\u306b\u306f \\(\\overrightarrow{x _ 0}\\) \u306b\u9650\u3089\u305a, \u4efb\u610f\u306e\u5217\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{x}\\) \u306b\u3064\u3044\u3066\r\n\\[\\begin{align}\r\nA^m \\overrightarrow{x} & = \\overrightarrow{x} \\\\\r\n\\text{\u2234} \\quad \\left( A^m -E \\right) \\overrightarrow{x} & = 0 \\\\\r\n\\text{\u2234} \\quad A^m & = E\r\n\\end{align}\\]<\/li>\r\n<\/ol>\r\n<p>\u4ee5\u4e0a\u3088\u308a, \\(A^m\\) \u306f\u5358\u4f4d\u884c\u5217\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u305f.<\/p>\r\n","protected":false},"excerpt":{"rendered":"\\(A\\) \u3092 \\(2\\) \u6b21\u306e\u6b63\u65b9\u884c\u5217\u3068\u3059\u308b. \u5217\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{x _ 0}\\) \u306b\u5bfe\u3057, \u5217\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{x _ 1} , \\overrightarro &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr200705\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[87],"tags":[140,109],"class_list":["post-614","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2007","tag-kyoto_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/614","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=614"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/614\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=614"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=614"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=614"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}