Studying Non-negative Factorizations with Tools from Linear Algebra over a Semiring

Abstract

We develop the technique useful for studying the problem of factoring nonnegative matrices. We illustrate our method, based on the tools from linear algebra over a semiring, by applying it to studying the problem of existence of a rank-three matrix with full nonnegative rank equal to n.

Key Words:

• Boolean matrices
• Gondran–Minoux rank
• Nonnegative factorization

2010 Mathematics Subject Classification:

• 15A23
• 15B35

Notes

Communicated by V. A. Artamonov.