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Almost orthogonal submatrices of an orthogonal matrix

Mark Rudelson
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Abstract

Let $A$ be an $n \times M$ matrix whose rows are orthonormal. Let $A_I$ be a submatrix of $A$ whose column indexes belong to the set $I$. Given $ε>0$ we estimate the smallest cardinality of the set $I$, such that the operator $A_I$ is an $ε$-isometry.

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Mark Rudelson. 1996-06-10. Almost orthogonal submatrices of an orthogonal matrix. https://arxiv.org/abs/math/9606213

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