標題: Diagonals and numerical ranges of direct sums of matrices 作者: Lee, Hsin-Yi應用數學系Department of Applied Mathematics 關鍵字: Numerical range;Direct sum;Compression 公開日期: 1-Nov-2013 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 partial derivative 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 circle plus 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). (C) 2013 Elsevier Inc. All rights reserved. URI: http://dx.doi.org/10.1016/j.laa.2013.07.019http://hdl.handle.net/11536/22677 ISSN: 0024-3795 DOI: 10.1016/j.laa.2013.07.019 期刊: LINEAR ALGEBRA AND ITS APPLICATIONS Volume: 439 Issue: 9 起始頁: 2584 結束頁: 2597 Appears in Collections: Articles

Files in This Item: