• Title, Summary, Keyword: commuting pair of matrices

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Commuting Pair Preservers of Matrices

  • Song, Seok-Zun;Oh, Jin-Young
    • Kyungpook Mathematical Journal
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    • v.47 no.2
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    • pp.277-281
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    • 2007
  • There are many papers on linear operators that preserve commuting pairs of matrices over fields or semirings. From these research works, we have a motivation to the research on the linear operators that preserve commuting pairs of matrices over nonnegative integers. We characterize the surjective linear operators that preserve commuting pairs of matrices over nonnegative integers.

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LINEAR MAPS THAT PRESERVE COMMUTING PAIRS OF MATRICES OVER GENERAL BOOLEAN ALGEBRA

  • SONG SEOK-ZUN;KANG KYUNG-TAE
    • Journal of the Korean Mathematical Society
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    • v.43 no.1
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    • pp.77-86
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    • 2006
  • We consider the set of commuting pairs of matrices and their preservers over binary Boolean algebra, chain semiring and general Boolean algebra. We characterize those linear operators that preserve the set of commuting pairs of matrices over a general Boolean algebra and a chain semiring.

A NOTE ON FLIP SYSTEMS

  • Lee, Sung-Seob
    • Honam Mathematical Journal
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    • v.29 no.3
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    • pp.341-350
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    • 2007
  • A dynamical system with a skew-commuting involution map is called a flip system. Every flip system on a subshift of finite type is represented by a pair of matrices, one of which is a permutation matrix. The transposition number of this permutation matrix is studied. We define an invariant, called the flip number, that measures the complexity of a flip system, and prove some results on it. More properties of flips on subshifts of finite type with symmetric adjacency matrices are investigated.