7 problems

Drew–Johnson–Loewy conjecture. The CP-rank of any completely positive matrix over $\mathbb{R}$ is at most

Let $m=ngeq4$, and let $\mathcal{S}_n$ denote the real symmetric $n\times n$ matrices. A linear operator $\mathcal{L}:\mathcal{S}_n\to\mathcal{S}_n$ preserves cp-rank if it maps ev…

Let $Q\in{\mathcal{CP}}^{n}$ be a rational matrix. A matrix $B\in{\mathcal{COP}}^{n}$ with $\langle B,Q\rangle<0$ certifies that $Q\notin{\mathcal{CP}}^{n}$, while a rational…

Berman–Shaked-Monderer's conjecture. Every integral matrix $A\in{\mathcal{CP}}^2$ possesses an integral cp-factorization.

Finite-termination conjecture. For $A\notin{\mathcal{CP}}^n$, Procedure with a suitable pivot rule in Step2(b) ends after finitely many iterations with a separating witness $W$.

SSymNMF-D conjecture. The decision problem SSymNMF-D is NP-hard.

Cp-rank upper-bound conjecture. Every completely positive matrix satisfies