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Czechoslovak Mathematical Journal

, Volume 56, Issue 2, pp 515–524 | Cite as

Perimeter preserver of matrices over semifields

  • Seok-Zun Song
  • Kyung-Tae Kang
  • Young-Bae Jun
Article
  • 28 Downloads

Abstract

For a rank-1 matrix A = ab t, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over semifields. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices over semifields if and only if it has the form T(A) = U AV, or T(A) = U A t V with some invertible matrices U and V.

Keywords

linear operator rank dominate perimeter (U, V)-operator 

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References

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    L. B. Beasley and N. J. Pullman: Boolean rank-preserving operators and Boolean rank-1 spaces. Linear Algebra Appl. 59 (1984), 55–77.MATHMathSciNetCrossRefGoogle Scholar
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    L. B. Beasley, S. Z. Song and S. G. Lee: Zero term rank preservers. Linear and Multilinear Algebra 48 (2001), 313–318.MATHMathSciNetGoogle Scholar
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    S. Z. Song, S. R. Park: Maximal column rank preservers of fuzzy matrices. Discuss. Math. Gen. Algebra Appl. 21 (2001), 207–218.MATHMathSciNetGoogle Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2006

Authors and Affiliations

  1. 1.Department of MathematicsCheju National UniversityJejuSouth Korea
  2. 2.Department of MathematicsGyeongsang National UniversityChinjuSouth Korea

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