Factorizations of matrices over semirings

✍ Scribed by Han Hyuk Cho; Suh-Ryung Kim

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 101 KB
• Volume: 373
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(03)00551-2

✦ Synopsis

In this paper, as a generalization of prime Boolean matrices and prime fuzzy matrices, we study semiprime matrices over chain semirings using the relationship between semiprime matrices and their row spaces. We show that a nonmonomial matrix with full semiring rank can be expressed as a product of elementary matrices and semiprime matrices. Furthermore, we show that a nonmonomial, regular matrix with full semiring rank can be expressed as a product of elementary matrices.