矩阵同时对角化为Hermite标准型的等价条件及推广

Equivalent Conditions and Generalizations of Matrix Diagonalization to Hermite Standard

本文给出两个矩阵同时对角化为Hermite标准型的一个等价条件.同时探讨了一个矩阵秩不等式的等号成立的一个充要条件.将给出一个单纯依靠矩阵方法和矩阵运算技巧的证明.然后对此命题作出一个直接推论.

In this paper, we give an equivalence condition of two matrices diagonalized to Hermite standard. At the same time, we discuss necessary and sufficient condition for the equal sign of a matrix rank inequality. We will give a proof of relying solely on matrix methods and matrix operations. And then make a direct conclusion on this proposition.