{"id":3421,"date":"2019-09-12T21:44:22","date_gmt":"2019-09-12T12:44:22","guid":{"rendered":"http:\/\/kogakubu.com\/?p=3421"},"modified":"2022-05-15T19:49:42","modified_gmt":"2022-05-15T10:49:42","slug":"%e3%80%90%e9%99%a2%e8%a9%a6%e5%af%be%e7%ad%96%e3%80%91%e7%b7%9a%e5%bd%a2%e4%bb%a3%e6%95%b0%e2%91%a5%ef%bc%88%e5%9b%ba%e6%9c%89%e5%80%a4%e3%81%a8%e5%9b%ba%e6%9c%89%e3%83%99%e3%82%af%e3%83%88%e3%83%ab","status":"publish","type":"post","link":"https:\/\/kogakubu.com\/?p=3421","title":{"rendered":"\u3010\u9662\u8a66\u5bfe\u7b56\u3011\u7dda\u5f62\u4ee3\u6570\u2465\uff08\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u305f\u884c\u5217\u306e\u5bfe\u89d2\u5316Part\uff12\uff09"},"content":{"rendered":"\n

\u3053\u3093\u306b\u3061\u306f\uff5e<\/p>\n

\u524d\u56de\u306e\u4e88\u544a\u901a\u308a\u3001\u4eca\u56de\u306f\u201c\u884c\u5217\u306e\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u305f\u884c\u5217\u306e\u5bfe\u89d2\u5316\u201d<\/span>\u306e\u4e2d\u3067\u3082\u5909\u63db\u884c\u5217\u306b\u76f4\u884c\u884c\u5217\u3092\u7528\u3044\u308b\u3082\u306e\u3002\u305d\u308c\u3082\u3001\u3082\u3068\u306f\u76f4\u4ea4\u884c\u5217\u3067\u306f\u306a\u3044\u3082\u306e\u3092\u7121\u7406\u3084\u308a\u76f4\u4ea4\u884c\u5217\u306b\u3057\u305f\u3068\u3044\u3046\u7279\u6b8a\u30d1\u30bf\u30fc\u30f3\u3064\u3044\u3066\u66f8\u3044\u3066\u3044\u304d\u305f\u3044\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n

\u305d\u308c\u3067\u306f\uff5e<\/p>\n

\u30b7\u30e5\u30ef\u30c3\u30c1\uff01<\/p>\n

\n

 <\/p>\n

\u7b2c\uff16\u56de\uff1a\u3010\u9662\u8a66\u5bfe\u7b56\u3011\u7dda\u5f62\u4ee3\u6570\u2465\uff08\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u305f\u884c\u5217\u306e\u5bfe\u89d2\u5316Part2\uff09<\/strong><\/p>\n

\u7b2c\uff16\u56de\u3082\u201d\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u305f\u884c\u5217\u306e\u5bfe\u89d2\u5316\u201d\u306b\u3064\u3044\u3066\u3067\u3059\u3002
\n\u3067\u3082\u3001\u5148\u306b\u3082\u66f8\u3044\u305f\u901a\u308a\u4eca\u56de\u306e\u306f\u4e00\u7656\u3042\u308b\u7279\u6b8a\u30d1\u30bf\u30fc\u30f3\u3067\u3059\uff01
\n\u305d\u308c\u306f\u5909\u63db\u884c\u5217\u306b\u76f4\u4ea4\u884c\u5217<\/span>\u3092\u7528\u3044\u308b\u30d1\u30bf\u30fc\u30f3\u3067\u3059\u3002<\/p>\n

\u524d\u56de\u306e\u8a18\u4e8b\u3067\u7d39\u4ecb\u3057\u305f\u901a\u308a\u3001\u884c\u5217\u306e\u5bfe\u89d2\u5316\u3067\u7528\u3044\u308b\u5909\u63db\u884c\u5217\u306f\u5fc5\u305a\u3057\u3082\u76f4\u4ea4\u884c\u5217\u3067\u3042\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\uff01
\n\u300c\u3058\u3083\u3042\u3001\u4f55\u306e\u305f\u3081\u306b\u76f4\u884c\u5316\u3059\u308b\u306e\u304b\u300d\u3063\u3066\uff1f<\/p>\n

\u3053\u308c\u306b\u3064\u3044\u3066\u306f\u50d5\u3082\u308f\u304b\u308a\u307e\u305b\u3093\uff08\u7b11\uff09
\n\u3067\u3082\u3001\u81ea\u5206\u306e\u5927\u5b66\u9662\u3067\u306f\u306a\u305c\u304b\u5909\u63db\u884c\u5217\u306b\u76f4\u884c\u884c\u5217\u3092\u4f7f\u308f\u305b\u305f\u304c\u308a\u307e\u3059\u30fb\u30fb\u30fb<\/p>\n

\u4eca\u56de\u306e\u8a08\u7b97\u3067\u5fc5\u8981\u3068\u306a\u308b\u77e5\u8b58\u306b\u3064\u3044\u3066\u306e\u904e\u53bb\u306e\u8a18\u4e8b\u306f\u3053\u3061\u3089\u2193
\n\u30fb\u3010\u9662\u8a66\u5bfe\u7b56\u3011\u7dda\u5f62\u4ee3\u6570\u2462\uff08\u884c\u5217\u306e\u548c\u7a4d\uff09<\/a>
\n\u30fb\u3010\u9662\u8a66\u5bfe\u7b56\u3011\u7dda\u5f62\u4ee3\u6570\u2463\uff08\u884c\u5217\u306e\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\uff09<\/a>
\n\u30fb\u3010\u9662\u8a66\u5bfe\u7b56\u3011\u7dda\u5f62\u4ee3\u6570\u2464\uff08\u56fa\u6709\u5024\u3068\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u7528\u3044\u305f\u884c\u5217\u306e\u5bfe\u89d2\u5316Part\uff11\uff09<\/a><\/p>\n

\u305d\u308c\u3067\u306f\u4eca\u56de\u3082\u4f8b\u984c\u3092\u4f7f\u3063\u305f\u6f14\u7fd2\u3067\u7406\u89e3\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u266a<\/p>\n

\uff1c\u4f8b\u984c\uff11\uff1e
\n\u4ee5\u4e0b\u306e\u884c\u5217A\u3092\u5909\u63db\u884c\u5217\u306b\u76f4\u4ea4\u884c\u5217\u3092\u7528\u3044\u3066\u3001\u5bfe\u89d2\u5316\u305b\u3088\u3002<\/p>\n

\\[
\nA = \\left(
\n\\begin{array}{ccc}
\n2 & 1 & 1 \\\\
\n1 & 2 & 1 \\\\
\n1 & 1 & 2
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\uff1c\u89e3\u6cd5\uff1e
\n\\begin{equation}
\nAX = \u03bbX\u3000\u3088\u308a\u3001\uff08A – \u03bbE\uff09X = 0
\n\\end{equation}<\/p>\n

\\[
\n\u3053\u3053\u3067\u3001T = A – \u03bbE = \\left(
\n\\begin{array}{ccc}
\n2 & 1 & 1 \\\\
\n1 & 2 & 1 \\\\
\n1 & 1 & 2
\n\\end{array}
\n\\right)
\n– \\left(
\n\\begin{array}{ccc}
\n\u03bb & 0 & 0 \\\\
\n0 & \u03bb & 0 \\\\
\n0 & 0 & \u03bb
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\\[
\n= \\left(
\n\\begin{array}{ccc}
\n2-\u03bb & 1 & 1 \\\\
\n1 & 2-\u03bb & 1 \\\\
\n1 & 1 & 2-\u03bb
\n\\end{array}
\n\\right)
\n\u3068\u304a\u304f\u3002
\n\\]<\/p>\n

\\begin{equation}
\n\u3059\u308b\u3068\u3001TX = 0\u30fb\u30fb\u30fb\u2460\u3067\u3042\u308a\u3001
\n\\end{equation}<\/p>\n

\\[
\n\\mathrm{det}T = |T| = \\left|
\n\\begin{array}{ccc}
\n2 – \u03bb & 1 & 1 \\\\
\n1 & 2 – \u03bb & 1 \\\\
\n1 & 1 & 2 – \u03bb
\n\\end{array}
\n\\right| = 0
\n\u3068\u306a\u308c\u3070\u3044\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002
\n\\]<\/p>\n

\\begin{equation}
\n= 1 + 1 + (2-\u03bb)^3 – (2-\u03bb) – (2-\u03bb) – (2 -\u03bb)
\n\\end{equation}<\/p>\n

\\begin{equation}
\n= 2 + 8 -8\u03bb+2\u03bb^2-4\u03bb+4\u03bb^2-\u03bb^3-6+3\u03bb
\n\\end{equation}<\/p>\n

\\begin{equation}
\n= -\u03bb^3+6\u03bb^2-9\u03bb+4
\n\\end{equation}<\/p>\n

\\begin{equation}
\n\u03bb^3-6\u03bb^2+9\u03bb-4=0
\n\\end{equation}<\/p>\n

\\begin{equation}
\n(\u03bb-1)(\u03bb^2-5\u03bb+4) = 0
\n\\end{equation}<\/p>\n

\\begin{equation}
\n(\u03bb-1)^2(\u03bb-4) = 0
\n\\end{equation}<\/p>\n

\\begin{equation}
\n\u3088\u3063\u3066\u3001\u56fa\u6709\u5024\u306f\u03bb = 1,4
\n\\end{equation}<\/p>\n

\u6b21\u306b\u305d\u308c\u305e\u308c\u306e\u56fa\u6709\u5024\u306b\u304a\u3051\u308b\u56fa\u6709\u30d9\u30af\u30c8\u30eb\u3092\u6c42\u3081\u307e\u3059\u3002
\n\\begin{equation}
\n\u2170)\u03bb = 1\u306e\u6642\u3001\u2460\u3092T_{1}X_{1}=0,
\n\\end{equation}
\n\\[
\nX_{1}=\\left(
\n\\begin{array}{ccc}
\n\u03b1_{1} \\\\
\n\u03b1_{2} \\\\
\n\u03b1_{3}
\n\\end{array}
\n\\right)
\n\u3068\u3059\u308b\u3068\u3001
\n\\]<\/p>\n

\\[
\n\\left(
\n\\begin{array}{ccc}
\n1 & 1 & 1\\\\
\n1 & 1 & 1 \\\\
\n1 & 1 & 1
\n\\end{array}
\n\\right)
\n\\left(
\n\\begin{array}{ccc}
\n\u03b1_{1}\\\\
\n\u03b1_{2}\\\\
\n\u03b1_{3}
\n\\end{array}
\n\\right)
\n= \\left(
\n\\begin{array}{ccc}
\n0\\\\
\n0\\\\
\n0
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\\begin{equation}
\n\u03b1_{1} + \u03b1_{2} + \u03b1_{3} = 0
\n\\end{equation}<\/p>\n

\\begin{equation}
\n\u03b1_{2}=k_{1},\u03b1_{3}=k_{2}\u3068\u3059\u308b\u3068\u3001\u03b1_{1}=-k_{1}-k_{2}\u3088\u308a\u3001\u56fa\u6709\u30d9\u30af\u30c8\u30ebX_{1}\u306f
\n\\end{equation}<\/p>\n

\\[
\nX_{1}=k_{1}\\left(
\n\\begin{array}{ccc}
\n-1 \\\\
\n1 \\\\
\n0
\n\\end{array}
\n\\right)
\n+k_{2}\\left(
\n\\begin{array}{ccc}
\n-1 \\\\
\n0 \\\\
\n1
\n\\end{array}
\n\\right)
\n\uff08k_{1},k_{2}\\neq0\uff09
\n\\]<\/p>\n

\\begin{equation}
\n\u2171)\u03bb = 4\u306e\u6642\u3001\u2460\u3092T_{2}X_{2}=0,
\n\\end{equation}
\n\\[
\nX_{2}=\\left(
\n\\begin{array}{ccc}
\n\u03b1_{4} \\\\
\n\u03b1_{5} \\\\
\n\u03b1_{6}
\n\\end{array}
\n\\right)
\n\u3068\u3059\u308b\u3068\u3001
\n\\]<\/p>\n

\\[
\n\\left(
\n\\begin{array}{ccc}
\n-2 & 1 & 1\\\\
\n1 & -2 & 1 \\\\
\n1 & 1 & -2
\n\\end{array}
\n\\right)
\n\\left(
\n\\begin{array}{ccc}
\n\u03b1_{4}\\\\
\n\u03b1_{5}\\\\
\n\u03b1_{6}
\n\\end{array}
\n\\right)
\n= \\left(
\n\\begin{array}{ccc}
\n0\\\\
\n0\\\\
\n0
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\\begin{eqnarray}
\n\\begin{cases}
\n-2\u03b1_{4} + \u03b1_{5} + \u03b1_{6} = 0 & \\\\
\n\u03b1_{4} -2\u03b1_{5} + \u03b1_{6} = 0 \\\\
\n\u03b1_{4} + \u03b1_{5} – 2\u03b1_{6} = 0
\n\\end{cases}
\n\\end{eqnarray}<\/p>\n

\\begin{equation}
\n\u03b1_{5}=k_{3}\u3068\u3059\u308b\u3068\u3001\u03b1_{4}=-k_{3},\u03b1_{6}=k_{3}\u3088\u308a\u3001\u56fa\u6709\u30d9\u30af\u30c8\u30ebX_{2}\u306f
\n\\end{equation}<\/p>\n

\\[
\nX_{2}=k_{3}\\left(
\n\\begin{array}{ccc}
\n1 \\\\
\n1 \\\\
\n1
\n\\end{array}
\n\\right)
\n\uff08k_{3}\\neq0\uff09
\n\\]<\/p>\n

\u4ee5\u4e0a\u3001\u2170\uff09\uff0c\u2171\uff09\u3088\u308a\u3001
\n\\[
\n\u5909\u63db\u884c\u5217P= \\left(
\n\\begin{array}{ccc}
\n-1 & -1 & 1 \\\\
\n1 & 0 & 1 \\\\
\n0 & 1 & 1
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\u3053\u308c\u306f\u305d\u308c\u305e\u308c\u306e\u5217\u30d9\u30af\u30c8\u30eb\u540c\u58eb\u3092\u201c\u884c\u5217\u306e\u548c\u7a4d\u201d\u3092\u7528\u3044\u3066\u8a08\u7b97\u3059\u308b\u3068\u30011\u5217\u76ee\u30682\u5217\u76ee\u306e\u548c\u7a4d\u304c\uff10\u306b\u306a\u3089\u306a\u3044\u306e\u3067\u76f4\u884c\u884c\u5217\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002
\n\u3067\u3059\u306e\u3067\u3001\u3053\u308c\u3092\u30b7\u30e5\u30df\u30c3\u30c8\u306e\u6b63\u898f\u76f4\u4ea4\u5316\u6cd5\u3092\u7528\u3044\u3066\u76f4\u4ea4\u5316\u3057\u307e\u3059\uff01<\/p>\n

\\[
\na_{1}=\\left(
\n\\begin{array}{ccc}
\n-1 \\\\
\n1 \\\\
\n0
\n\\end{array}
\n\\right)
\n,a_{2}=\\left(
\n\\begin{array}{ccc}
\n-1 \\\\
\n0 \\\\
\n1
\n\\end{array}
\n\\right)
\n,a_{3}=\\left(
\n\\begin{array}{ccc}
\n1 \\\\
\n1 \\\\
\n1
\n\\end{array}
\n\\right)
\n\u3068\u304a\u304f\u3002
\n\\]<\/p>\n

\\begin{equation}
\n\u2460u_{1}=\\frac{1}{||a_{1}||}a_{1}
\n\\end{equation}<\/p>\n

\\[
\n=\\frac{1}{\\sqrt{2}} \\left(
\n\\begin{array}{c}
\n-1 \\\\
\n1 \\\\
\n0
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\\[
\n\u2461b_{2} = a_{2} – \\sum_{k=1}^1 (u_{k}\u30fba_{2})u_{k}
\n\\]<\/p>\n

\\begin{equation}
\n=a_{2}-(u_{1}\u30fba_{2})u_{1}
\n\\end{equation}<\/p>\n

\\[
\n=\\left(
\n\\begin{array}{ccc}
\n-1 \\\\
\n0 \\\\
\n1
\n\\end{array}
\n\\right)
\n– \\frac{1}{2}
\n\\left(
\n\\begin{array}{ccc}
\n-1 \\\\
\n1 \\\\
\n0
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\\[
\n=- \\frac{1}{2} \\left(
\n\\begin{array}{ccc}
\n1 \\\\
\n1 \\\\
\n-2
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\\begin{equation}
\nu_{2}=\\frac{1}{||b_{2}||}b_{2}
\n\\end{equation}<\/p>\n

\\[
\n=\\frac{-1}{\\sqrt{6}} \\left(
\n\\begin{array}{c}
\n1 \\\\
\n1 \\\\
\n-2
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\\[
\n\u2462b_{3} = a_{3} – \\sum_{k=1}^2 (u_{k}\u30fba_{3})u_{k}
\n\\]<\/p>\n

\\begin{equation}
\n=a_{3}-{(u_{1}\u30fba_{3})u_{1}+(u_{2}\u30fba_{3})u_{2}}
\n\\end{equation}<\/p>\n

\\[
\n=\\left(
\n\\begin{array}{ccc}
\n1 \\\\
\n1 \\\\
\n1
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\\begin{equation}
\nu_{3}=\\frac{1}{||b_{3}||}b_{3}
\n\\end{equation}<\/p>\n

\\[
\n=\\frac{1}{\\sqrt{3}} \\left(
\n\\begin{array}{c}
\n1 \\\\
\n1 \\\\
\n1
\n\\end{array}
\n\\right)
\n\\]<\/p>\n

\u3088\u3063\u3066\u3001\u5909\u63db\u884c\u5217P\u306f
\n\\[
\nP= \\left(
\n\\begin{array}{ccc}
\n\\frac{-1}{\\sqrt{2}} & \\frac{-1}{\\sqrt{6}} & 1 \\\\
\n\\frac{1}{\\sqrt{2}} & \\frac{-1}{\\sqrt{6}} & 1 \\\\
\n0 & \\frac{2}{\\sqrt{6}} & 1
\n\\end{array}
\n\\right)
\n\u3068\u76f4\u4ea4\u884c\u5217\u306b\u5909\u63db\u3067\u304d\u305f\u3002
\n\\]<\/p>\n

\u5bfe\u89d2\u5316\u3057\u305f\u884c\u5217\u306f<\/p>\n

\"\"<\/p>\n

\n

\u3010\u30b7\u30e5\u30df\u30c3\u30c8\u306e\u6b63\u898f\u76f4\u884c\u5316\u6cd5\u3011<\/p>\n

\\begin{equation}
\n\u4e00\u822c\u306e\u57fa\u5e95(a_{1},a_{2},a_{3},\u30fb\u30fb\u30fb,a_{n})\u306b\u3064\u3044\u3066\u3001
\n\\end{equation}<\/p>\n

\\begin{equation}
\n\u2170)m = 1\u306e\u6642\u3001
\nu_{1}=\\frac{1}{||a_{1}||}a_{1}
\n\\end{equation}<\/p>\n

\\[
\n\u2171)2\\le m\\le n\u306e\u6642\u3001
\n\\]<\/p>\n

\\begin{equation}
\nb_{m} = a_{m} – \\sum_{k=1}^{m-1} (u_{k}\u30fba_{m})u_{k}
\n\\end{equation}<\/p>\n

\\begin{equation}
\nu_{m}=\\frac{1}{||b_{m}||}b_{m}
\n\\end{equation}<\/p>\n

\u4ee5\u4e0a\u3088\u308a\u3001\u30b7\u30e5\u30df\u30c3\u30c8\u306e\u6b63\u898f\u76f4\u4ea4\u5316\u6cd5\u5f8c\u306e\u5909\u63db\u884c\u5217\u306f
\n\\begin{equation}
\nP=(u_{1},u_{2},\u30fb\u30fb\u30fb,u_{n})
\n\\end{equation}<\/p>\n<\/div>\n

\n

 <\/p>\n

\u3044\u304b\u304c\u3067\u3057\u305f\u3067\u3057\u3087\u3046\u304b\uff1f<\/p>\n

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