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


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.


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


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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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