教師資料查詢 | 類別: 期刊論文 | 教師: 譚必信 Tam Bit-shun (瀏覽個人網頁)

標題:Nonnegative square roots of matrices
學年104
學期2
出版(發表)日期2016/06/01
作品名稱Nonnegative square roots of matrices
作品名稱(其他語言)
著者Bit-ShunTam; Peng-RueiHuang
單位
出版者
著錄名稱、卷期、頁數Linear Algebra and its Applications 498, pp.404-440
摘要By the square root of a (square) matrix A we mean a matrix B that satisfies B2=A. In this paper, we begin a study of the (entrywise) nonnegative square roots of nonnegative matrices, adopting mainly a graph-theoretic approach. To start with, we settle completely the question of existence and uniqueness of nonnegative square roots for 2-by-2 nonnegative matrices. By the square of a digraph H , denoted by H2, we mean the digraph with the same vertex set as H such that (i,j) is an arc if there is a vertex k such that (i,k) and (k,j) are both arcs in H. We call a digraph H a square root of a digraph G if H2=G. It is observed that a necessary condition for a nonnegative matrix to have a nonnegative square root is that its digraph has a square root, and also that a digraph G has a square root if and only if there exists a nonnegative matrix A with digraph G such that A has a nonnegative square root. We consider when or whether certain kinds of digraphs (including digraphs that are disjoint union of directed paths and circuits, permutation digraphs or a special kind of bigraphs) have square roots. We also consider when certain kinds of nonnegative matrices (including monomial matrices, rank-one matrices and nilpotent matrices with index two) have nonnegative square roots. A known characterization of loopless digraphs to have square roots, due to F. Escalantge, L. Montejano, and T. Rojano, is extended (and amended) to digraphs possibly with loops. Some natural open questions are also posed.
關鍵字Nonnegative matrix;Nonnegative square root;Square root of digraph;Permutation digraph;Bigraph;Monomial matrices;Nilpotent matrix;Rank-one matrix
語言英文(美國)
ISSN0024-3795;1873-1856
期刊性質國外
收錄於SCI;
產學合作
通訊作者Bit-Shun Tam
審稿制度
國別美國
公開徵稿
出版型式,電子版,紙本
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