A simplex algorithm for rational cp-factorization
Mathieu Dutour Sikiri\'c, Achill Sch\"urmann, Frank Vallentin

TL;DR
This paper introduces a simplex-like algorithm that computes rational cp-factorizations of matrices, demonstrating that all integral 2x2 completely positive matrices have integral cp-factorizations, thus advancing understanding of matrix factorizations.
Contribution
The paper presents a novel simplex algorithm for rational cp-factorization, providing a constructive method and proving integral factorizations exist for 2x2 matrices.
Findings
Algorithm successfully finds rational cp-factorizations
All integral 2x2 completely positive matrices have integral cp-factorizations
Provides a new approach to matrix factorization problems
Abstract
In this paper we provide an algorithm, similar to the simplex algorithm, which determines a rational cp-factorization of a given matrix, whenever the matrix allows such a factorization. This algorithm can be used to show that every integral completely positive matrix has an integral cp-factorization.
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