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 en_US
ISSN 0024-3795 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 是
國別 USA
公開徵稿
出版型式 ,電子版,紙本
相關連結

機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/106937 )