# Zero-dilation index of Sn-matrix and companion matrix

Hwa Long Gau, Pei Yuan Wu

## 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 (Formula presented), where 0k denotes the k-by-k zero matrix. In this paper, it is shown that if A is an Sn-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 Sn-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.

原文 ???core.languages.en_GB??? 47 666-678 13 Electronic Journal of Linear Algebra 31 1 https://doi.org/10.13001/1081-3810.3193 已出版 - 2016

## 指紋

• ### Sn矩陣與伴同矩陣的零延拓指數之研究

Gau, H.

1/08/1631/07/17

研究計畫: Research