关于扰动正定矩阵行列式的不等式
Inequalities with Determinants of Perturbed Positive Matrices
摘要：
本文证明了关于正定矩阵$A$的行列式与其扰动矩阵$A+D$的行列式之比$\det(A+D)/\det A$的两个不等式。在第一个问题中，我们研究了正矩阵加到原矩阵的对角块上时所发生的扰动。在第二个问题中，扰动被添加到矩阵的逆。
英文摘要：
We prove two inequalities regarding the ratio $\det(A+D)/\det A$ of the determinant of a positive-definite matrix $A$ and the determinant of its perturbation $A+D$. In the first problem, we study the perturbations that happen when positive matrices are added to diagonal blocks of the original matrix. In the second problem, the perturbations are added to the inverses of the matrices.
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