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LINEAR OPERATORS THAT PRESERVE SETS OF PRIMITIVE MATRICES

  • Beasley, Leroy B. ;
  • Kang, Kyung-Tae ;
  • Song, Seok-Zun
  • Received : 2013.11.20
  • Published : 2014.07.01

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

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)