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5.2 二次型的标准形与规范形 - PowerPoint PPT Presentation


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5.2 二次型的标准形与规范形. 二次型的标准形 :. 标准形的矩阵 :. 将二次型化为标准形 :. 1. 配方法. 2. 正交变换法. 正交变换:. 2. 初等变换法. 方法:. 命题 1 二次型的标准形不唯一. 命题 2 任一二次型都可经可逆的线性变换化为规范形:. 秩: 正惯性指数: 负惯性指数: 符号差:. 矩阵 A 的正、负惯性指数. 定理 5.4 (惯性定理)任一二次型都可经可逆的线性变换化为 规范形,且规范性唯一. 5.2 over.

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5.2 二次型的标准形与规范形

二次型的标准形:

标准形的矩阵:



2. 正交变换法

正交变换:


2. 初等变换法

方法:


命题1 二次型的标准形不唯一.

命题2 任一二次型都可经可逆的线性变换化为规范形:

秩:

正惯性指数:

负惯性指数:

符号差:

矩阵 A的正、负惯性指数


定理5.4(惯性定理)任一二次型都可经可逆的线性变换化为

规范形,且规范性唯一.



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