矩阵Hadamard积和乘积的若干范数不等式

Some Norm Inequalities for Hadamard Products and Conventional Products of Matrices

文章研究矩阵Hadamard积及普通乘积的酉不变范数与谱范数的不等式。利用分块矩阵的技巧及矩阵特征值的优超理论,得到一系列关于矩阵乘积和Hadamard积的范数不等式,改进Zhan的一个结果,同时推广关于Horn和Mathias的矩阵酉不变范数的Cauchy-Schwarz不等式。

Some inequalities of the unitary invariant norm and spectral norm on Hadamard products and conventional products of matrices are studied. By applying the techniques of block matrices,and the majorization theory of matrix eigenvalues,a series of norm inequalities for Hadamard products and conventional products of matrices are obtained. Among them,the result due to Zhan is improved by obtaining some inequalities.Meanwhile,this paper also gives a generalization of Cauchy-Schwarz inequality for the unitary invariant norm due to Horn and Mathias.