Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2013.11.20
  • Published : 2014.07.01
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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 ${\varepsilon}_{n^2-2n+1}$.

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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