A trace inequality for positive definite matrices

2010/11/20 by E. Veronica Belmega, Samson Lasaulce, Belmega, E. V. +3
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1011.6325

openalex publication_date 2010/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove that Tr (MN+ PQ)>= 0 when the following two conditions are met: (i) the matrices M, N, P, Q are structured as follows: M = A -B, N = inv(B)-inv(A), P = C-D, Q =inv (B+D)-inv(A+C), where inv(X) denotes the inverse matrix of X (ii) A, B are positive definite matrices and C, D are positive semidefinite matrices.

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