LINEAR OPERATORS THAT PRESERVE SETS OF PRIMITIVE MATRICES

Title & Authors
LINEAR OPERATORS THAT PRESERVE SETS OF PRIMITIVE MATRICES
Beasley, Leroy B.; Kang, Kyung-Tae; Song, Seok-Zun;

Abstract
We consider linear operators on square matrices over antinegative semirings. Let $\small{{\varepsilon}_k}$ denote the set of all primitive matrices of exponent k. We characterize those linear operators which preserve the set $\small{{\varepsilon}_1}$ and the set $\small{{\varepsilon}_2}$, and those that preserve the set $\small{{\varepsilon}_{n^2-2n+2}}$ and the set $\small{{\varepsilon}_{n^2-2n+1}}$. We also characterize those linear operators that strongly preserve $\small{{\varepsilon}_2}$, $\small{{\varepsilon}_{n^2-2n+2}}$ or $\small{{\varepsilon}_{n^2-2n+1}}$.
Keywords
Linear operator;primitive matrix;line matrix;double star matrix;
Language
English
Cited by
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