標題: Diagonals and numerical ranges of weighted shift matrices 作者: Wang, Kuo-ZhongWu, Pei Yuan應用數學系Department of Applied Mathematics 關鍵字: Numerical ranges;Weighted shift matrix;Compression 公開日期: 1-一月-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. For any such compression, we give a standard model under unitary equivalence for A. This is then applied to determine the value of k(A) for A of size 3 in terms of the shape of W (A). When A is a matrix of the form (0 W-1 ... 0 ... w(n-1) w(n) 0 ), we show that k(A) = n if and only if either vertical bar w(1)vertical bar = ... = vertical bar w(n)vertical bar or n is even and vertical bar w(1)vertical bar = vertical bar w(3)vertical bar = ... = vertical bar w(n-1)vertical bar and vertical bar w(2)vertical bar = vertical bar w(4)vertical bar = ... = lwn For such matrices A with exactly one of the wi's zero, we show that any k, 2 <= k <= n - 1, can be realized as the value of k(A), and determine exactly when the equality k(A) = n - 1 holds. (C) 2012 Elsevier Inc. All rights reserved. URI: http://dx.doi.org/10.1016/j.laa.2012.08.007http://hdl.handle.net/11536/20803 ISSN: 0024-3795 DOI: 10.1016/j.laa.2012.08.007 期刊: LINEAR ALGEBRA AND ITS APPLICATIONS Volume: 438 Issue: 1 起始頁: 514 結束頁: 532 顯示於類別： 期刊論文