The square root theorem for positive semidefinite matrices and their monotonicity

2023/05/17 by Aouichaoui, Mohamed Amine, Mortad, Mohammed Hichem
Computer Science · Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Inequalities and Applications #Mathematics and Applications #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2305.11187

openalex publication_date 2023/05/17 · openalex created_date 2023/05/23 · openalex updated_date 2026/07/28

Abstract

In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.

Related

• New properties for certain positive semidefinite matrices
• Positive matrices partitioned into a small number of Hermitian blocks
• Real square roots of matrices: differential properties in semi-simple, symmetric and orthogonal cases
• On Drury's solution of Bhatia & Kittaneh's question
• On a decomposition lemma for positive semi-definite block-matrices