標題: Structures and numerical ranges of power partial isometries 作者: Gau, Hwa-LongWu, 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-Jan-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.2013.11.013http://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 Appears in Collections: Articles

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