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for questions involving inequalities, upper and lower bounds.

3 votes
Accepted

A conjecture about the submatrix of orthogonal matrix

Neither conjecture is true in general, as seen from the following counterexample for $n = 4$, $k = 2$, and \begin{align} U = \begin{pmatrix} 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & \frac{1}{\sqrt{2 …
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