The integer cp-rank of $2 \times 2$ matrices

TL;DR

This paper establishes an upper bound of 11 on the cp-rank for integer doubly nonnegative 2x2 matrices, providing a key insight into their structural complexity.

Contribution

It proves a new upper bound on the cp-rank specifically for integer 2x2 doubly nonnegative matrices, advancing understanding in matrix factorization.

Findings

cp-rank of integer 2x2 doubly nonnegative matrices does not exceed 11

Provides a theoretical limit on the complexity of such matrices

Enhances knowledge of matrix factorization bounds

Abstract

We show the cp-rank of an integer doubly nonnegative $2 \times 2$ matrix does not exceed $11$.