Diagonals and numerical ranges of direct sums of matrices

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109185

Title:	Diagonals and numerical ranges of direct sums of matrices
Authors:	李信儀;Lee, Hsin-Yi
Contributors:	理學院數學系
Keywords:	Compression;Direct sum;Numerical range
Date:	2013-11-01
Issue Date:	2026-04-23 16:14:02 (UTC+8)
Publisher:	Elsevier Inc.;Elsevier Inc
Abstract:	摘要： For any n-by-n matrix A, we consider the maximum number k=k(A) for which there is a k-by-k compression of A with all its diagonal entries in the boundary ∂W(A) of the numerical range W(A) of A. If A is a normal or a quadratic matrix, then the exact value of k(A) can be computed. For a matrix A of the form B⊕C, we show that k(A)=2 if and only if the numerical range of one summand, say, B is contained in the interior of the numerical range of the other summand C and k(C)=2. For an irreducible matrix A, we can determine exactly when the value of k(A) equals the size of A. These are then applied to determine k(A) for a reducible matrix A of size 4 in terms of the shape of W(A). 出版者： Elsevier Inc 出版日期： 2013-11-01 出處： Linear algebra and its applications, 2013-11, Vol.439 (9), p.2584-2597 資源來源： Elsevier ScienceDirect Journals AutoHoldings 版權： 2013 Elsevier Inc. 識別號： ISSN: 0024-3795 識別號： EISSN: 1873-1856 識別號： DOI: 10.1016/j.laa.2013.07.019
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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