- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 Isolation numbers of integer matrices and their preservers Bull. Korean Math. Soc. 2020 Vol. 57, No. 3, 535-545 https://doi.org/10.4134/BKMS.b180210Published online May 31, 2020 LeRoy B. Beasley, Kyung-Tae Kang, Seok-Zun Song Utah State University; Jeju National University; Jeju National University Abstract : 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 $A$. Keywords : Isolation number, upper ideal, linear operator, $(P,Q)$-operator MSC numbers : 15A86, 15A04, 15A33 Supported by : This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(No.2016R1D1A1B02006812). Downloads: Full-text PDF   Full-text HTML