# ISOLATION NUMBERS OF INTEGER MATRICES AND THEIR PRESERVERS

• Beasley, LeRoy B. (Department of Mathematics and Statistics Utah State University) ;
• Kang, Kyung-Tae (Department of Mathematics Jeju National University) ;
• Song, Seok-Zun (Department of Mathematics Jeju National University)
• Received : 2018.03.09
• Accepted : 2018.12.18
• Published : 2020.05.31

#### 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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