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第8章二次型

第8章二次型

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2008 春季班 线性代数 8 二次型 8 1 第8章 二次型 8.1 二次型与二次型的矩阵 n 个变量的二次齐次多项式 ∑∑ = = = n i n j j i ij n x x a x x x f 1 1 2 1 ) , , , ( " 称为 n 元二次型. 二次型有3种表达形式: (1) 完全展开式 ) , , , ( 2 1 n x x x f " = n n x x a x x a x a 1 1 2 1 12 2 1 11 + + + " n n x x a x a x x a 2 2 2 2 22 1 2 21 + + + + " " " + 2 2 2 1 1 n nn n n n n x a x x a x x a " + + + (2) 和式 ∑∑ = = = n i n j j i ij n x x a x x x f 1 1 2 1 ) , , , ( " ji ij a a = (3) 矩阵表达式 T n x x x x ) , , , ( 2 1 " = ( ) ij a A = ji ij a a =
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