3 problems

Let $M\in\mathbb R^{p\times q}_{\geq 0}$ have rank $k+1$ and satisfy … Let $P$ and $Q$ be the two polytopes corresponding to $M$ in the nested-polytope representation. Spectrahedro…

Rank-one factor abundance conjecture. Every such matrix has a psd factorization in which either at least $k$ matrices $A_i$ and $k-1$ matrices $B_j$ are rank one, or at least $k-1$…

Let $M$ be a matrix represented as a slack matrix $M=S_{P,Q}$ of nested polytopes $P\subseteq Q\subseteq\mathbb R^{r-1}$. A spectrahedral shadow $C$ of size $k$ between $P$ and $Q$…