Integrally normalizable matrices with respect to a given set

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• 作者：Sudipta Mallik^a ; ^{sudipta.mallik@nau.edu" class="auth_mail" title="E-mail the corresponding author} ; Bryan L. Shader^b ; ^{bshader@uwyo.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：15B36 ; 05C20 ; 05C50
• 刊名：Linear Algebra and its Applications
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：498
• 期：Complete
• 页码：317-325
• 全文大小：295 K

文摘

The class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515004012&_mathId=si1.gif&_user=111111111&_pii=S0024379515004012&_rdoc=1&_issn=00243795&md5=b9e152023dd6ce86b404570e77913121" title="Click to view the MathML source">n×nclass="mathContainer hidden">class="mathCode">$n\times n$ matrix A is integrally normalizable with respect to a prescribed subset M   of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379515004012&_mathId=si2.gif&_user=111111111&_pii=S0024379515004012&_rdoc=1&_issn=00243795&md5=20288dcee29be043eb34c7fb10a1faff" title="Click to view the MathML source">{(i,j):i,j=1,2,…,n and i≠j}class="mathContainer hidden">class="mathCode">$\{(i,j):i,j=1,2,\dots ,n\text{and}i\ne j\}$ provided A is diagonally similar to an integer matrix each of whose entries in positions corresponding to M is equal to 1. In the case that the elements of M form the arc set of a spanning tree, the matrices that are integrally normalizable with respect to M have been characterized. This paper gives a characterization for general subsets M. In addition, necessary and sufficient conditions for each matrix with a given zero–nonzero pattern to be integrally normalizable with respect to an arbitrary subset M are given.