標題: Structures and numerical ranges of power partial isometries
作者: Gau, Hwa-Long
Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
關鍵字: Partial isometry;Power partial isometry;Numerical range;S-n-matrix;Jordan block
公開日期: 1-一月-2014
摘要: We derive a matrix model, under unitary similarity, of an n-by-n matrix A such that A, A(2),, A(k) (k >= 1) are all partial isometries, which generalizes the known fact that if A is a partial isometry, then it is unitarily similar to a matrix of the form [(0 B)(0 C)] with B*B +C*C =1. Using this model, we show that if A has ascent k and A, A(2),..., Ak(-1) are partial isometries, then the numerical range W (A) of A is a circular disc centered at the origin if and only if A is unitarily similar to a direct sum of Jordan blocks whose largest size is k. As an application, this yields that, for any S-n-matrix A, W (A) (resp., W (A circle times A)) is a circular disc centered at the origin if and only if A is unitarily similar to the Jordan block J(n). Finally, examples are given to show that, for a general matrix A, the conditions that W (A) and W (A circle times A) are circular discs at 0 are independent of each other. (C) 2013 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.laa.2013.11.013
http://hdl.handle.net/11536/23640
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.11.013
期刊: LINEAR ALGEBRA AND ITS APPLICATIONS
Volume: 440
Issue: 
起始頁: 325
結束頁: 341
顯示於類別:期刊論文


文件中的檔案:

  1. 000329557700026.pdf