Integer completely positive matrices of order two

TL;DR

This paper proves that all integer doubly nonnegative 2x2 matrices can be factored into integer completely positive matrices, establishing a fundamental property of such matrices.

Contribution

It demonstrates that every integer doubly nonnegative 2x2 matrix admits an integer cp-factorization, a novel result in matrix theory.

Findings

All integer 2x2 doubly nonnegative matrices have integer cp-factorizations.

The result extends understanding of matrix factorizations in low dimensions.

Provides a basis for exploring similar factorizations in higher dimensions.

Abstract

We show that every integer doubly nonnegative $2 \times 2$ matrix has an integer cp-factorization.