Zhi-Qiang Xu

Optimal Condition Numbers in Low-Rank Positive Semidefinite Matrix Sensing

In this paper we focus on the stability of positive semidefinite matrix sensing maps $\Phi_{\mathcal{A}}(X)=(\langle A_i,X\rangle)_{i=1}^m$ where $A_i\succeq 0$, $X\succeq0$ and $\operatorname{rank}(X)\le r$. We introduce the bi-Lipschitz constants of $\Phi_{\mathcal{A}}(X)$ and define the global condition numbers as t...