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4
votes
Partitioning an orthogonal matrix into full rank square submatrices
Thanks so much, Federico. That was very helpful. In case others are interested, this problem was also studied in the more general context of matroid theory in
C. Greene, "A multiple exchange propert …
4
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2
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Partitioning an orthogonal matrix into full rank square submatrices
Let $U$ be an $n \times n$ orthogonal matrix. Given an arbitrary partition ${\mathcal P}_c=\{y_1,y_2,\ldots,y_k\}$ of the columns of
$U$, does there always exist a corresponding partition ${\mathcal …