Some Hadamard product inequalities for accretive matrices

2023/07/06 by Alemeh Sheikhhosseini, Sheikhhosseini, A., Somayeh Malekinejad +3
Engineering · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2307.02838

openalex publication_date 2023/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain some new matrix inequalities involving Hadamard product. Also some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps and matrix concave functions are investigated. Among other results, it is shown that if A, B, C, D are n× n positive definite matrices, then (αA+βB)^r∘(αC+βD)^1-r≤ α(A^r∘ C^1-r)+β(B^r∘ D^1-r), where r ∈ (-1, 0) ∪ (1, 2) and " ∘ " stands for the Hadamard product.

Related

• Some new bounds for the Hadamard product and the Fan product of matrices
• From positive to accretive matrices
• On the weighted Geometric mean of accretive matrices
• Further Properties of Accretive Matrices
• Matrix inequalities and majorizations around Hermite-Hadamard's inequality