Abstract
Abstract 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.
Highlights
1 Introduction Throughout the paper, we assume Cm×n is the set of m × n complex matrices, I is a identity matrix, Eii is a diagonal matrix with at its (i, i)th position and elsewhere, and Zn = [E, E, . . . , Enn]∗ ∈ Cn ×n is a selection matrix
A∗ stands for the conjugate transpose of
The matrix A is Hermitian if A∗ = A, denoted by A ∈ H(n)
Summary
Meixiang Chen[1,2], Qinghua Chen[2], Zhongpeng Yang1,3*, Xiaoxia Feng[3] and Zhixing Lin[1]
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