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Recall that the power partial isometry index $p(A)$ of a matrix $A$ is the supremum, possibly infinity, of nonnegative integers $j$ such that $I, A, A^2, \\ldots, A^j$ are all partial isometries while the ascent $a(A)$ of $A$ is the smallest integer $k\\ge 0$ for which $\\ker A^k$ equals $\\ker A^{k+1}$. 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