[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2014.51.4.773

LINEAR OPERATORS THAT PRESERVE SETS OF PRIMITIVE MATRICES

Beasley, Leroy B. (Department of Mathematics and Statistics Utah State University)
Kang, Kyung-Tae (Department of Mathematics Jeju National University)
Song, Seok-Zun (Department of Mathematics and Research Institute for Basic Sciences Jeju National University)

Publication Information

Journal of the Korean Mathematical Society / v.51, no.4, 2014 , pp. 773-789 More about this Journal

Abstract

We consider linear operators on square matrices over antinegative semirings. Let ${\varepsilon}_k$ denote the set of all primitive matrices of exponent k. We characterize those linear operators which preserve the set ${\varepsilon}_1$ and the set ${\varepsilon}_2$ , and those that preserve the set ${\varepsilon}_{n^2-2n+2}$ and the set ${\varepsilon}_{n^2-2n+1}$ . We also characterize those linear operators that strongly preserve ${\varepsilon}_2$ , ${\varepsilon}_{n^2-2n+2}$ or ${\varepsilon}_{n^2-2n+1}$ .

Keywords

Linear operator; primitive matrix; line matrix; double star matrix;

Citations & Related Records

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