A Unified Theorem on SDP Rank Reduction

We consider the problem of finding a low-rank approximate solution to a system of linear equations in symmetric, positive semidefinite matrices. Specifically, let $A_1,\ldots,A_m \in \R^{n\times n}$ be symmetric, positive semidefinite matrices, and let $b_1,\ldots,b_m \ge 0$. We show that if there exists a symmetric, positive semidefinite matrix $X$ to the system $A_i \bullet X … Read more