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Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2009; 46(2): 373-385

Printed March 1, 2009

https://doi.org/10.4134/BKMS.2009.46.2.373

Copyright © The Korean Mathematical Society.

Boolean regular matrices and their strongly preservers

Seok-Zun Song, Kyung-Tae Kang, and Mun-Hwan Kang

Jeju National University

Abstract

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An $m\times n$ Boolean matrix $A$ is called regular if there exists an $n\times m$ Boolean matrix $X$ such that $AXA=A$. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices.

Keywords: Boolean algebra, generalized inverse of a matrix, regular matrix, $(U,V)$-operator

MSC numbers: 15A04, 15A09

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