A. Yu. Mikhalev, I. V. Oseledets
Published 2015-02-27Version 1
A definition of $p$-volume of rectangular matrices is given. We generalize the results for square maximum-volume submatrices to the case rectangular maximal-volume submatrices and provide estimates for the growth of the coefficients. Three promising applications of such submatrices are presented: recommender systems, finding maximal elements in low-rank matrices and preconditioning of overdetermined linear systems. The code is available online at \url{https://bitbucket.org/muxas/rect_maxvol}.
Comments: 11 pages, 1 figure, submitted to SIAM J. Matrix Analysis
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