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arXiv · 1011.6325

A trace inequality for positive definite matrices

E. V. Belmega·S. Lasaulce·M. Debbah
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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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E. V. Belmega, S. Lasaulce, M. Debbah. 2010-11-20. A trace inequality for positive definite matrices. https://arxiv.org/abs/1011.6325

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