I have a $k$ by $n$ matrix $A$, with $k \ll n$. In case it helps, the $k$ rows are orthonormal.

I'm interested in finding a $k$ by $k$ orthogonal matrix $M$ so as to maximize the $L^{\infty}$ norms of the rows of $MA$. This is a little imprecise, since it may not be possible to maximize all of them simultaneously. At the moment, my criterion is to maximize the weighted sums of these $L^{\infty}$ norms by some weights $w_{1}, \ldots, w_{k}$. All of these weights are fairly similar, so if it is easier, I would also be happy with maximizing the average.

This seems to be a little bit similar to PCA, which essentially finds rows with maximal L^2 norm.

Thanks for any suggestions/literature references.