標題: ZERO-DILATION INDEX OF S-n-MATRIX AND COMPANION MATRIX
作者: Gau, Hwa-Long
Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
關鍵字: Zero-dilation index;S-n-Matrix;Companion matrix;Numerical range.
公開日期: 1-十月-2016
摘要: The zero-dilation index d(A) of a square matrix A is the largest k for which A is unitarily similar to a matrix of the form [GRAPHICS] , where 0(k) denotes the k-by-k zero matrix. In this paper, it is shown that if A is an S-n-matrix or an n-by-n companion matrix, then d (A) is at most. [n/2], the smallest integer greater than or equal to n/2. Those A's for which the upper bound is attained are also characterized. Among other things, it is shown that, for an odd n, the S-n-matrix A is such that d (A) = (n + 1) /2 if and only if A is unitarily similar to -A, and, for an even n, every n-by-n companion matrix A has d (A) equal to n/2.
URI: http://dx.doi.org/10.13001/1081-3810.3193
http://hdl.handle.net/11536/144586
ISSN: 1537-9582
DOI: 10.13001/1081-3810.3193
期刊: ELECTRONIC JOURNAL OF LINEAR ALGEBRA
Volume: 31
起始頁: 666
結束頁: 678
顯示於類別:期刊論文