When does cp-rank equal rank?

TL;DR

This paper investigates conditions under which a completely positive matrix has equal cp-rank and rank, providing sufficient criteria and an efficient algorithm for verification.

Contribution

It introduces new easy-to-check conditions for doubly nonnegative matrices to be completely positive with equal cp-rank and rank, along with an efficient algorithm.

Findings

Sufficient conditions for equality of cp-rank and rank.

An algorithm demonstrating the practical verification of these conditions.

Enhanced understanding of the structure of completely positive matrices.

Abstract

The problem of finding completely positive matrices with equal cp-rank and rank is considered. We give some easy-to-check sufficient conditions on the entries of a doubly nonnegative matrix for it to be completely positive with equal cp-rank and rank. An algorithm is also presented to show its efficiency.