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#7 第2章附加题2

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opened 3 years ago by 黄定江 · 0 comments
黄定江 commented 3 years ago

设 阶对称阵 是正定的，去掉方针 的第 行第 列的子矩阵记为 ，记 ，则 在 条件下的最小值为 ，其中 。

设 ![](https://render.githubusercontent.com/render/math?math=n) 阶对称阵 ![](https://render.githubusercontent.com/render/math?math=A) 是正定的，去掉方针 ![](https://render.githubusercontent.com/render/math?math=A) 的第 ![](https://render.githubusercontent.com/render/math?math=i) 行第 ![](https://render.githubusercontent.com/render/math?math=i) 列的子矩阵记为 ![](https://render.githubusercontent.com/render/math?math=A_i)，记 ![](https://render.githubusercontent.com/render/math?math=Q(x)=x^TAx,\hspace{0.1em}x\in\mathbb{R}^n)，则 ![](https://render.githubusercontent.com/render/math?math=Q(x)) 在 ![](https://render.githubusercontent.com/render/math?math=x_i=1) 条件下的最小值为 ![](https://render.githubusercontent.com/render/math?math=\frac{det(A)}{det(A_i)})，其中 ![](https://render.githubusercontent.com/render/math?math=x=(x_1,x_2,\cdots,x_n)^T)。
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向量和矩阵基础
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