{"id":90281,"date":"2023-11-19T19:02:29","date_gmt":"2023-11-19T19:02:29","guid":{"rendered":"https:\/\/science-hub.click\/%E3%83%91%E3%83%83%E3%82%BB%E3%83%BC%E3%82%B8%E3%83%9E%E3%83%88%E3%83%AA%E3%83%83%E3%82%AF%E3%82%B9-%E5%AE%9A%E7%BE%A9\/"},"modified":"2023-11-19T19:02:29","modified_gmt":"2023-11-19T19:02:29","slug":"%E3%83%91%E3%83%83%E3%82%BB%E3%83%BC%E3%82%B8%E3%83%9E%E3%83%88%E3%83%AA%E3%83%83%E3%82%AF%E3%82%B9-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=90281","title":{"rendered":"\u30d1\u30c3\u30bb\u30fc\u30b8\u30de\u30c8\u30ea\u30c3\u30af\u30b9 – \u5b9a\u7fa9"},"content":{"rendered":"

\u30d1\u30b9\u884c\u5217\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001<\/strong>\u30d9\u30af\u30c8\u30eb\u3001\u6e96\u540c\u578b\u3001\u53cc\u7dda\u5f62\u5f62\u5f0f\u306e\u884c\u5217\u8868\u73fe\u306e\u57fa\u5e95\u5909\u5316\u516c\u5f0f\u3092\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>

\u610f\u5473<\/span><\/h2>

\u3055\u305b\u3066

$$ {\\mathbb K} $$<\/div>\u30dc\u30c7\u30a3\u3001E \u306f K \u30d9\u30af\u30c8\u30eb\u7a7a\u9593\u3067\u3059\u3002<\/p>

\u62e0\u70b9\u304c2\u3064\u3042\u308b\u3068\u3057\u3088\u3046

$$ {B=(e_1 \\dots e_n)} $$<\/div>\u305d\u3057\u3066
$$ {B’=(e’_1 \\dots e’_n)} $$<\/div>\u8a18\u61b6\u4e0a\u306e\u7406\u7531\u304b\u3089\u3001 B<\/i> ‘<\/span>\u3092\u65b0\u3057\u3044\u5869\u57fa\u3001 B \u3092<\/i><\/span>\u53e4\u3044\u5869\u57fa\u3068\u307f\u306a\u3057\u307e\u3059\u3002<\/p>

\u3057\u305f\u304c\u3063\u3066\u3001 B<\/i><\/span>\u304b\u3089B<\/i> ‘<\/span>\u3078\u306e\u901a\u904e\u884c\u5217<\/a><\/span><\/strong>\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002 $$ {P_B^{B’}} $$<\/p><\/div> :

$$ {P_B^{B’} = (a_{i,j})_{i,j=1}^n \\in \\mathcal M_n(\\mathbb K)} $$<\/div>\u306e\u3088\u3046\u306a
$$ {\\forall j \\in [\\![1,n]\\!], \\quad e’_j=\\sum_{i=1}^n a_{i,j}e_i} $$<\/div><\/dd><\/dl>

\u3053\u306e\u884c\u5217\u306e\u5217\u306f\u3001\u53e4\u3044\u57fa\u6570\u3067\u8868\u73fe\u3055\u308c\u305f\u65b0\u3057\u3044\u57fa\u6570\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8868\u3059\u884c\u5217\u3067\u3059\u3002<\/p>

\n\"\u30d1\u30c3\u30bb\u30fc\u30b8\u30de\u30c8\u30ea\u30c3\u30af\u30b9<\/figure>

\u307e\u305f\u3001\u901a\u904e\u884c\u5217\u3092\u3001\u57fa\u5e95B<\/i> ‘<\/span>\u3092\u5099\u3048\u305fE<\/i>\u304b\u3089\u57fa\u5e95B<\/i><\/span>\u3092\u5099\u3048\u305fE<\/i>\u3078\u306e\u6052\u7b49\u5199\u50cf<\/a><\/span>\u3092\u8868\u3059\u884c\u5217\u3068\u3057\u3066\u89e3\u91c8\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u6211\u3005\u306f\u6301\u3063\u3066\u3044\u307e\u3059

$$ {P_B^{B’}=\\mathcal M_{B’B}(\\mathrm{Id}_E)} $$<\/div>\u307e\u305f\u306f
$$ {\\mathcal M_{B’B}(\\mathrm{Id}_E)} $$<\/div>\u306f\u3001 B<\/i> ‘<\/span>\u304a\u3088\u3073B<\/i><\/span>\u306b\u5bfe\u3059\u308bId E<\/i><\/sub><\/span>\u306e\u884c\u5217\u3067\u3059\u3002<\/p>
\n\"\u30d1\u30c3\u30bb\u30fc\u30b8\u30de\u30c8\u30ea\u30c3\u30af\u30b9<\/figure>

\u5b9a\u7406<\/span><\/span><\/h2>

\u58f0\u660e<\/span><\/h3>

\u30d9\u30af\u30c8\u30eb\u3092<\/a><\/span>\u307f\u307e\u3057\u3087\u3046

$$ {x \\in E} $$<\/div> \u3001\u305d\u308c\u305e\u308c\u306e\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u3092\u6301\u3061\u307e\u3059
$$ {X=\\begin{bmatrix} x_1 \\\\ \\vdots \\\\ x_n \\end{bmatrix}} $$<\/div>\u305d\u3057\u3066
$$ {X’=\\begin{bmatrix} x’_1 \\\\ \\vdots \\\\ x’_n \\end{bmatrix}} $$<\/div> 2 \u3064\u306e\u5869\u57faB<\/i><\/span>\u3068B<\/i> ‘<\/span>\u3067\u3059\u3002<\/p>

\u305d\u308c\u3067

$$ {X=P_{B}^{B’}X’} $$<\/div><\/p>

\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<\/a><\/span><\/span><\/h3>

\u30d9\u30af\u30c8\u30eb\u3092 2 \u3064\u306e\u5869\u57fa\u306b\u5206\u89e3\u3059\u308b\u3068<\/a><\/span>\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002

$$ {x=\\sum_{j=1}^n x_j e_j=\\sum_{j=1}^n x’_j e’_j} $$<\/div><\/p>

\u3055\u3089\u306b\u3001

$$ {\\forall j \\in [\\![1,n]\\!], e’_j=\\sum_{i=1}^n a_{i,j}e_i} $$<\/div><\/p>
\n\"\u30d1\u30c3\u30bb\u30fc\u30b8\u30de\u30c8\u30ea\u30c3\u30af\u30b9<\/figure>

\u7f6e\u304d\u63db\u3048\u308b\u3068\u3001 <\/p>

$$ {x=\\sum_{j=1}^n x’_j \\sum_{i=1}^n a_{i,j}e_i} $$<\/div><\/dd><\/dl>
$$ {x=\\sum_{i=1}^n \\left(\\sum_{j=1}^n a_{i,j} x’_j\\right) e_i} $$<\/div><\/dd><\/dl>

\u30d9\u30af\u30c8\u30eb\u306e\u5206\u89e3\u306f\u5404\u5869\u57fa\u3067\u4e00\u610f\u3067\u3042\u308b\u305f\u3081\u3001\u4fc2\u6570\u306e\u7279\u5b9a\u306b\u9032\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {\\forall i \\in [\\![1,n]\\!], x_i=\\sum_{j=1}^n a_{i,j} x’_j = \\left(P_B^{B’}\\cdot X’\\right)_i} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001
$$ {X=P_B^{B’}X’} $$<\/div><\/dd><\/dl>

\u53ef\u9006\u6027<\/span><\/h2>

B<\/i><\/span>\u3068B<\/i> ‘ \u3092<\/span>E \u306e 2 \u3064\u306e\u5869\u57fa\u3068\u3059\u308b\u3068\u3001

$$ {P_B^{B’}} $$<\/div>\u53cd\u8ee2\u53ef\u80fd\u3067\u3042\u308a\u3001
$$ {\\left(P_B^{B’}\\right)^{-1}=P_{B’}^B} $$<\/div><\/p>

\u30c7\u30e2\u30f3\u30b9\u30c8\u30ec\u30fc\u30b7\u30e7\u30f3<\/span><\/h3>
$$ {P_B^{B’}P_{B’}^B=\\mathcal M_{B’,B}(\\mathrm{Id}_E)\\mathcal M_{B,B’}(\\mathrm{Id}_E) = M_{B,B}(\\mathrm{Id}_E) = I_n} $$<\/div><\/dd><\/dl><\/div>\n

\u53c2\u8003\u8cc7\u6599<\/h2>\n
  1. \u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u0642\u0627\u0639\u062f\u0629 (\u062c\u0628\u0631 \u062e\u0637\u064a) \u2013 arabe<\/a><\/li>
  2. Canvi de base \u2013 catalan<\/a><\/li>
  3. Matice p\u0159echodu \u2013 tch\u00e8que<\/a><\/li>
  4. Basiswechsel (Vektorraum) \u2013 allemand<\/a><\/li>
  5. Change of basis \u2013 anglais<\/a><\/li>
  6. \u015can\u011do de bazo \u2013 esp\u00e9ranto<\/a><\/li><\/ol>\n
    \n

    \n \u30d1\u30c3\u30bb\u30fc\u30b8\u30de\u30c8\u30ea\u30c3\u30af\u30b9 – \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n