The further generalization on the inequalities for Hadamard products of any number of invertible Hermitian matrices

Journal of inequalities and applications

Meixiang Chen¹ 

关键词: Hermitian matrix;    Hadamard product;    matrix inequality;    equation condition;   

DOI  :  10.1186/1029-242X-2014-479

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Without ‘positive definiteness’ demanded in the present papers, the forward and reverse inequalities for Hadamard products of any number of invertible Hermitian matrices are obtained, and the sufficient and necessary conditions for the equations in these inequalities are given. As Hermitian positive matrices naturally satisfy the added constraints, these results generalize and improve the corresponding results in the present papers. Beyond that, with no demand of ‘positive definiteness’, these forward and backward inequalities are not determined mutually any longer.

【 授权许可】

CC BY