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A trace inequality for positive definite matrices

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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https://hal.archives-ouvertes.fr/hal-00446982
Contributor : Elena Veronica Belmega <>
Submitted on : Wednesday, January 13, 2010 - 7:08:21 PM
Last modification on : Wednesday, April 8, 2020 - 3:26:22 PM
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  • HAL Id : hal-00446982, version 1

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Elena Veronica Belmega, Samson Lasaulce, Merouane Debbah. A trace inequality for positive definite matrices. Journal of Inequalities in Pure and Applied Mathematics (JIPAM), 2009, 10 (1), 4 p. ⟨hal-00446982⟩

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