A Unified Theorem on Sdp Rank Reduction

Abstract

We consider the problem of finding a low{rank approximate solution to a system of linearequations in symmetric, positive semidefinite matrices. Specifically, let A1; : : : ;Am 2 Rn£n symmetric, positive semidefinite matrices, and let b1; : : : ; bm ¸ 0. We show that if there exists a symmetric, positive semidefinite matrix X to the following system of equations: