#11 第4章附加题2

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opened 3 years ago by 黄定江 · 0 comments

证明:若 是对称的,而且其前 个顺序主子阵均非奇异,则 有唯一的分解式

其中 是单位下三角矩阵, 是对角矩阵。

证明:若 ![](https://render.githubusercontent.com/render/math?math=A\in\mathbb{R}^{n\times{n}}) 是对称的,而且其前 ![](https://render.githubusercontent.com/render/math?math=n-1) 个顺序主子阵均非奇异,则 ![](https://render.githubusercontent.com/render/math?math=A) 有唯一的分解式 ![](https://render.githubusercontent.com/render/math?math=A=LDL^T,) 其中 ![](https://render.githubusercontent.com/render/math?math=L) 是单位下三角矩阵,![](https://render.githubusercontent.com/render/math?math=D) 是对角矩阵。
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矩阵分解
label 3 years ago
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