{"id":61283,"date":"2024-01-28T17:35:45","date_gmt":"2024-01-28T17:35:45","guid":{"rendered":"https:\/\/science-hub.click\/%E4%BA%8C%E6%AC%A1%E5%BD%A2%E5%BC%8F-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-01-28T17:35:45","modified_gmt":"2024-01-28T17:35:45","slug":"%E4%BA%8C%E6%AC%A1%E5%BD%A2%E5%BC%8F-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"http:\/\/science-hub.click\/?p=61283","title":{"rendered":"\u4e8c\u6b21\u5f62\u5f0f – \u5b9a\u7fa9"},"content":{"rendered":"

\u6570\u5b66\u3067\u306f\u3001\u4e8c\u6b21\u5f62\u5f0f\u306f<\/strong>\u4efb\u610f\u306e\u6570\u306e\u5909\u6570\u3092\u542b\u3080 2 \u6b21\u306e\u540c\u6b21\u591a\u9805\u5f0f\u3067\u3059\u3002\u305f\u3068\u3048\u3070\u30013 \u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u5185\u306e 2 \u70b9\u9593\u306e\u8ddd\u96e2\u306f\u30012 \u70b9\u306e\u305d\u308c\u305e\u308c\u306e 3 \u3064\u306e\u5ea7\u6a19\u3067\u3042\u308b 6 \u3064\u306e\u5909\u6570\u3092\u542b\u30802 \u6b21\u5f62\u5f0f<\/a><\/span>\u306e\u5e73\u65b9\u6839<\/a><\/span>\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u53d6\u5f97\u3055\u308c\u307e\u3059\u3002<\/p>

1 \u3064\u30012 \u3064\u3001\u304a\u3088\u3073 3 \u3064\u306e\u5909\u6570\u306e\u4e8c\u6b21\u5f62\u5f0f\u306f\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {F(x) = ax^2\\,} $$<\/div><\/dd>
$$ {F(x,y) = ax^2 + by^2 + 2cxy\\,} $$<\/div><\/dd>
$$ {F(x,y,z) = ax^2 + by^2 + cz^2 + 2dxy + 2exz + 2fyz\\,} $$<\/div><\/dd><\/dl>

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Q<\/i>\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3:

$$ {V \\to F} $$<\/div>\u5bfe\u79f0\u53cc\u4e00\u6b21\u5f62\u5f0f<\/a><\/span>B<\/i>\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001 \u306fV<\/i>\u4e0a\u306e\u4e8c\u6b21\u5f62\u5f0f<\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002
$$ {V \\times V \\to F} $$<\/div>\u306e\u3088\u3046\u306a<\/p>
$$ {Q(u) = B(u,u)\\,} $$<\/div>
$$ {\\forall u \\in V\\,} $$<\/div><\/dd><\/dl>

B \u306f<\/i>\u95a2\u9023\u53cc\u7dda\u5f62<\/a><\/span>\u5f62\u5f0f<\/strong>\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u3069\u306e<\/a><\/span>\u30d9\u30af\u30c8\u30eb<\/a><\/span>\u306b\u3064\u3044\u3066\u3082\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044

$$ {u,v \\in V\\,} $$<\/div><\/p>
$$ {Q(u + v) = Q(u) + 2B(u,v) + Q(v)\\,} $$<\/div><\/dd><\/dl>

\u3057\u305f\u304c\u3063\u3066\u3001 Q<\/i>\u304b\u3089\u53cc\u4e00\u6b21\u5f62\u5f0fB \u3092<\/i>\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 <\/p>

$$ {B(u,v) = \\frac{1}{2}\\left(Q(u+v) – Q(u) – Q(v)\\right)} $$<\/div><\/dd><\/dl>

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V<\/i>\u304cn<\/i>\u6b21\u5143<\/a><\/span>\u306e\u5834\u5408\u3001\u53cc\u4e00\u6b21\u5f62\u5f0fB \u3092<\/i>\u3042\u308b\u57fa\u5e95\u3092\u57fa\u6e96\u3068\u3057\u305f\u5bfe\u79f0\u884c\u5217<\/a><\/span>B<\/strong>\u3068\u3057\u3066\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002

$$ {\\{e_i\\}\\,} $$<\/div> V<\/i>\u306e\u5834\u5408\u3002 B<\/strong>\u306e\u6210\u5206\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002
$$ {B_{ij} = B(e_i,e_j)\\,} $$<\/div> \u3002\u4e8c\u6b21\u5f62\u5f0fQ \u306f<\/i>\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059<\/span>\u3002 <\/p>
$$ {Q(u) = \\mathbf{u}^T \\mathbf{Bu} = \\sum_{i,j=1}^{n}B_{ij}u^i u^j} $$<\/div><\/dd><\/dl>

\u307e\u305f\u306f

$$ {u^i\\,} $$<\/div>\u306f\u3053\u306e\u57fa\u5e95\u306b\u304a\u3051\u308bu<\/i>\u306e\u6210\u5206\u3067\u3059\u3002\u6700\u521d\u306e\u5b9a\u7fa9<\/a><\/span>\u306b\u5f93\u3063\u3066\u3001 Q<\/i> ( u<\/i> ) \u306fu<\/i>\u306e\u5ea7\u6a19\u306b\u304a\u3051\u308b\u6b21\u6570<\/span>2 \u306e\u540c\u6b21\u591a\u9805\u5f0f<\/a><\/span>\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>

\u4e8c\u6b21\u5f62\u5f0f\u306e\u305d\u306e\u4ed6\u306e\u30d7\u30ed\u30d1\u30c6\u30a3: <\/p>