A trace inequality for positive definite matrices
Functional Analysis
2010-11-30 v1
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.
Keywords
Cite
@article{arxiv.1011.6325,
title = {A trace inequality for positive definite matrices},
author = {E. V. Belmega and S. Lasaulce and M. Debbah},
journal= {arXiv preprint arXiv:1011.6325},
year = {2010}
}