# Rational factorizations of completely positive matrices

## TL;DR

This paper proves that any rational matrix inside the cone of completely positive matrices can be factored into rational matrices, ensuring rational cp-factorizations exist within the interior of this cone.

## Contribution

It establishes that all rational matrices in the interior of the completely positive cone admit rational cp-factorizations, filling a gap in the understanding of matrix factorizations.

## Key findings

- Rational matrices in the interior have rational cp-factorizations
- The result applies to all matrices within the interior of the cone
- Provides a constructive proof for rational factorizations

## Abstract

In this note it is proved that every rational matrix which lies in the interior of the cone of completely positive matrices also has a rational cp-factorization.