Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ISOLATION NUMBERS OF INTEGER MATRICES AND THEIR PRESERVERS

  • Received : 2018.03.09
  • Accepted : 2018.12.18
  • Published : 2020.05.31
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Abstract

Let A be an m × n matrix over nonnegative integers. The isolation number of A is the maximum number of isolated entries in A. We investigate linear operators that preserve the isolation number of matrices over nonnegative integers. We obtain that T is a linear operator that strongly preserve isolation number k for 1 ≤ k ≤ min{m, n} if and only if T is a (P, Q)-operator, that is, for fixed permutation matrices P and Q, T(A) = P AQ or, m = n and T(A) = P AtQ for any m × n matrix A, where At is the transpose of A.

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References

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