关于矩阵奇异值分解的注记

Remarks on the Singular Value Decomposition of Matrix

利用矩阵的奇异值分解及奇异值与特征值关系,研究矩阵的主对角线元素、矩阵的迹、矩阵的表示、矩阵的谱范数及范数与矩阵奇异值之间的关系,获得了矩阵的迹的实部与矩阵的奇异值的关系、矩阵的Frobenius范数与矩阵奇异值等式关系及矩阵是正规矩阵的充要条件。

This article is based on singular value decomposition of matrix and the related proper- ties of the singular value and characteristic value. Firstly, the product of matrix trace and matrix trace of real part and the relationship between matrix singular value are studied and some results are obtained; secondly, the necessary and sufficient conditions of matrix are explored. Lastly, Frobenius norm of the matrix and the singular value and the relationship between characteristic values are researched.