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Given a m-by-n matrix with $n>>m$ and with a known rank of $k\leq m$, what would be a computationally effective way of finding out $k$ columns, such that the matrix formed using these $k$ columns has the best condition number?

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Something to consider: Use some heuristic to select one or two columns, and then do Gram Schmidt orthonormalization to guess the best candidates for the rest. Gerhard "Ask Me About Dumb Guessing" Paseman, 2013.04.26 – Gerhard Paseman Apr 26 '13 at 15:56
seems to be a duplicate of:… – Suvrit Apr 26 '13 at 17:24

Finding this subset of columns is a non-trivial task, but some approximate answers are known. For details and pointers, please refer to my answer here.

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