Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LINEAR MAPS THAT PRESERVE COMMUTING PAIRS OF MATRICES OVER GENERAL BOOLEAN ALGEBRA

  • SONG SEOK-ZUN (Department of Mathematics Cheju National University) ;
  • KANG KYUNG-TAE (Department of Mathematics Cheju National University)
  • Published : 2006.01.01
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Abstract

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.

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References

  1. L. B. Beasley, Linear transformations on matrices: the invariance of commuting pairs of matrices, Linear Multilinear Algebra 6 (1978/79), no. 3, 179-183
  2. G. H. Chan and M. H. Lim, Linear transformations on symmetric matrices that preserve commutativity, Linear Algebra Appl. 47 (1982), 11-22 https://doi.org/10.1016/0024-3795(82)90222-1
  3. M. D. Choi, A. A. Jafarian, and H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227-241 https://doi.org/10.1016/0024-3795(87)90169-8
  4. S. Kirkland and N. J. Pullman, Linear operators preserving invariants of non-binary matrices, Linear Multilinear Algebra 33 (1992), no. 3-4, 295-300 https://doi.org/10.1080/03081089308818200
  5. H. Radjavi, Commutativity-preserving operators on symmetric matrices, Linear Algebra Appl. 61 (1984), 219-224 https://doi.org/10.1016/0024-3795(84)90032-6
  6. S. Z. Song and L. B. Beasley, Linear operators that preserve commuting pairs of nonnegative real matrices, Linear Multilinear Algebra 51 (2003), no. 3, 279-283 https://doi.org/10.1080/0308108031000084383
  7. S. Z. Song and S. G. Lee, Column ranks and their preserver of general Boolean matrices, J. Korean Math. Soc. 32 (1995), no. 3, 531-540
  8. W. Watkins, Linear maps that preserve commuting pairs of matrices, Linear Al-gebra Appl. 14 (1976), no. 1, 29-35 https://doi.org/10.1016/0024-3795(76)90060-4

Cited by

  1. EXTREME SETS OF RANK INEQUALITIES OVER BOOLEAN MATRICES AND THEIR PRESERVERS vol.28, pp.1, 2013, https://doi.org/10.4134/CKMS.2013.28.1.001