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 |