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${\scriptsize\left[\begin{array}{cc} 0_k & \ast\\ \ast & \ast\end{array}\right]}$ , 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$\lceil n/2\rceil$ , 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$n/2$ 出版日期： 2016-02-05 出處： The Electronic journal of linear algebra, 2016-02, Vol.31, p.666-678 資源來源： Alma/SFX Local Collection 識別號： ISSN: 1081-3810 識別號： ISSN: 1537-9582 識別號： EISSN: 1081-3810 識別號： DOI: 10.13001/1081-3810.3193
