Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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RANK AND PERIMETER PRESERVERS OF BOOLEAN RANK-1 MATRICES

  • Song, Seok-Zun (Department of Mathematics Cheju National University) ;
  • Beasley, Leroy-B. (Department of Mathematics and Statistics Utah State University) ;
  • Cheon, Gi-Sang (Department of Mathematics Daejin University) ;
  • Jun, Young-Bae (Department of Mathematics Education Gyeongsang National University)
  • Published : 2004.03.01
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Abstract

For a Boolean rank-l matrix $A\;=\;ab^{t}$, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the Boolean linear operators that preserve rank and perimeter of Boolean rank-l matrices.

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References

  1. Linear Algebra Appl. v.59 Boolean rank preserving operators and Bollean rank-1 spaces L.B.Beasley;N.J.Pullman https://doi.org/10.1016/0024-3795(84)90158-7
  2. Linear Multillinear Algebra v.48 Zero term rank preservers L.B.Beasley;S.Z.Song;S.G.Lee https://doi.org/10.1080/03081080108818677
  3. J. Combin. Inform. System Sci. v.8 Semiring rank : Boolean rank and nonnegative rank factorizations D.A.Gregory;N.J.Pullman
  4. Pure Appl. Math. v.70 Boolean Matrix Theory and Applications K.H.Kim

Cited by

  1. On linear operators strongly preserving invariants of Boolean matrices vol.62, pp.1, 2012, https://doi.org/10.1007/s10587-012-0004-y
  2. The arctic rank of a Boolean matrix vol.433, 2015, https://doi.org/10.1016/j.jalgebra.2015.03.005
  3. Linear Preservers of Perimeters of Nonnegative Real Matrices vol.48, pp.3, 2008, https://doi.org/10.5666/KMJ.2008.48.3.465