대한수학회지 (Journal of the Korean Mathematical Society)

  • 제43권3호
  • /
  • Pages.539-552
  • /
  • 2006
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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LINEAR PRESERVERS OF BOOLEAN NILPOTENT MATRICES

  • Song, Seok-Zun (Department of Mathematics Cheju National University) ;
  • Kang, Kyung-Tae (Department of Mathematics Cheju National University) ;
  • Jun, Young-Bae (Department of Mathematics Education Gyeongsang National University)
  • 발행 : 2006.05.01
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초록

For an $n{\times}n$ Boolean matrix A, A is called nilpotent if $A^m=O$ for some positive integer m. We consider the set of $n{\times}n$ nilpotent Boolean matrices and we characterize linear operators that strongly preserve nilpotent matrices over Boolean algebras.

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참고문헌

  1. L. B. Beasley and N. J. Pullman, Boolean rank preserving operators and Boolean rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77 https://doi.org/10.1016/0024-3795(84)90158-7
  2. L. B. Beasley and N. J. Pullman, Operators that preserve semiring matrix functions, Linear Algebra Appl. 99 (1988), 199-216 https://doi.org/10.1016/0024-3795(88)90132-2
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  5. S. Kirkland and N. J. Pullman, Linear operators preserving invariants of non- binary matrices, Linear Multilinear Algebra 33 (1993), 295-300
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  7. S. -Z. Song and S. -G. Lee, Column ranks and their preservers of general Boolean matrices, J. Korean Math. Soc. 32 (1995), no. 3, 531-540

피인용 문헌

  1. Regular matrices and their strong preservers over semirings vol.429, pp.1, 2008, https://doi.org/10.1016/j.laa.2008.02.015
  2. The Invertible Linear Operator Preserving {1,2}-Inverses of Matrices over Semirings vol.05, pp.01, 2015, https://doi.org/10.12677/PM.2015.51002
  3. Primitive symmetric matrices and their preservers vol.65, pp.1, 2017, https://doi.org/10.1080/03081087.2016.1175414
  4. Zero-term rank and zero-star cover number of symmetric matrices and their linear preservers vol.64, pp.12, 2016, https://doi.org/10.1080/03081087.2016.1155534
  5. On linear operators strongly preserving invariants of Boolean matrices vol.62, pp.1, 2012, https://doi.org/10.1007/s10587-012-0004-y