摘要： We give a complete characterization of nonnegative integers j and k and a positive integer n for which there is an n-by-n matrix with its power partial isometry index equal to j and its ascent equal to k. Recall that the power partial isometry index p(A) of a matrix A is the supremum, possibly infinity, of nonnegative integers j such that I,A,A2,…,Aj are all partial isometries while the ascent a(A) of A is the smallest integer k≥0 for which kerAk equals kerAk+1. It was known before that, for any matrix A, either p(A)≤min{a(A),n−1} or p(A)=∞. In this paper, we prove more precisely that there is an n-by-n matrix A such that p(A)=j and a(A)=k if and only if one of the following conditions holds: (a) j=k≤n−1, (b) j≤k−1 and j+k≤n−1, or (c) j≤k−2 and j+k=n. This answers a question we asked in a previous paper. 出版者： Elsevier Inc 出版日期： 2014-10-15 出處： Linear algebra and its applications, 2014-10, Vol.459, p.136-144 資源來源： Elsevier ScienceDirect Journals 版權： 2014 Elsevier Inc. 識別號： ISSN: 0024-3795 識別號： EISSN: 1873-1856 識別號： DOI: 10.1016/j.laa.2014.07.001
