Power partial isometry index and ascent of a finite matrix

@article{Gau2013PowerPI,
  title={Power partial isometry index and ascent of a finite matrix},
  author={Hwa-Long Gau and P. Wu},
  journal={Linear Algebra and its Applications},
  year={2013},
  volume={459},
  pages={136-144}
}
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 ker⁡Ak equals ker⁡Ak+1. It was known before that, for… Expand
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