Regular matrices and their strong preservers over semirings

✍ Scribed by Seok-Zun Song; Kyung-Tae Kang; LeRoy B. Beasley; Nung-Sing Sze

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 181 KB
• Volume: 429
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2008.02.015

✦ Synopsis

An m × n matrix A over a semiring S is called regular if there is an n × m matrix G over S such that AGA = A. We study the problem of characterizing those linear operators T on the matrices over a semiring such that T (X) is regular if and only if X is. Complete characterizations are obtained for many semirings including the Boolean algebra, the nonnegative reals, the nonnegative integers and the fuzzy scalars.