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Let $A$ be an $m\times n$ 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 $1\le k\le \min\{m,n\}$ if and only if $T$ is a ($P,Q$)-operator, that is, for fixed permutation matrices $P$ and $Q$, $T(A) = PAQ$ or, $m=n$ and $T(A) = PA^t Q$ for any $m\times n$ matrix $A$, where $A^t $ is the transpose of $A$.
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참고문헌 (14)
참고문헌 신청
LeRoy B. Beasley / 2012 / Isolation number versus Boolean rank / Linear Algebra and its Applications 436(9):3469~3474
L. B. Beasley / 2017 / Preservers of upper ideals of matrices : Tournaments; Primitivity / J. Combin. Math. Combin. Comput 100:55~75
LeRoy B. Beasley / 1985 / Nonnegative rank-preserving operators / Linear Algebra and its Applications 65:207~223
LeRoy B. Beasley / 2018 / Possible isolation number of a matrix over nonnegative integers / Czechoslovak Mathematical Journal 68(4):1055~1066
LeRoy B. Beasley / 1984 / Boolean-rank-preserving operators and Boolean-rank-1 spaces / Linear Algebra and its Applications 59:55~77
L. B. Beasley / 2017 / Preservers of upper ideals of matrices : Tournaments; Primitivity / J. Combin. Math. Combin. Comput 100:55~75
LeRoy B. Beasley / 1985 / Nonnegative rank-preserving operators / Linear Algebra and its Applications 65:207~223
LeRoy B. Beasley / 2018 / Possible isolation number of a matrix over nonnegative integers / Czechoslovak Mathematical Journal 68(4):1055~1066
LeRoy B. Beasley / 1984 / Boolean-rank-preserving operators and Boolean-rank-1 spaces / Linear Algebra and its Applications 59:55~77
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