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- W2189496613 abstract "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,A 2 ,...,A j are all partial isometries while the ascent a(A) of A is the smallest integer k ≥ 0 for which kerA k equals kerA k+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, and (c) j ≤ k − 2 and j + k = n. This answers a question we asked in a previous paper." @default.
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- W2189496613 date "2013-01-01" @default.
- W2189496613 modified "2023-09-27" @default.
- W2189496613 title "Power Partial Isometry Index and Ascent of a" @default.
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- W2189496613 hasPublicationYear "2013" @default.
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