A trace inequality for positive definite matrices

Details A trace inequality for positive definite matrices A trace inequality for positive definite matrices

2010-11-20

arxiv.org/abs/1011.6325v1

Mathematics

Functional Analysis

Scientific paper

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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