Numerical radii for tensor products of matrices

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109243

Title:	Numerical radii for tensor products of matrices
Authors:	高華隆;Gau, Hwa-Long;Wang, Kuo-Zhong;Wu, Pei Yuan
Contributors:	理學院數學系
Keywords:	Algebra;Blocking;Discs;Mathematical analysis;matrix;nonnegative matrix;Norms;numerical radius;numerical range;Operators (mathematics);Origins;tensor product
Date:	2015-01-01
Issue Date:	2026-04-23 16:17:53 (UTC+8)
Publisher:	Taylor and Francis Ltd.;Abingdon: Taylor & Francis
Abstract:	摘要： For -by- and -by- complex matrices and , it is known that the inequality holds, where and denote, respectively, the numerical radius and the operator norm of a matrix. In this paper, we consider when this becomes an equality. We show that (1) if and , then one of the following two conditions holds: (i) has a unitary part, and (ii) is completely nonunitary and the numerical range of is a circular disc centered at the origin, (2) if for some , , then , and, moreover, the equality holds if and only if is unitarily similar to the direct sum of the -by- Jordan block and a matrix with , and (3) if is a nonnegative matrix with its real part (permutationally) irreducible, then , if and only if either or and is permutationally similar to a block-shift matrix with , where and . 出版者： Abingdon: Taylor & Francis 出版日期： 2015-10-03 出處： Linear & multilinear algebra, 2015-10, Vol.63 (10), p.1916-1936 版權： 2013 Taylor & Francis 2013 版權： 2013 Taylor & Francis 識別號： ISSN: 0308-1087 識別號： EISSN: 1563-5139 識別號： DOI: 10.1080/03081087.2013.839669
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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