Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898073 | Linear Algebra and its Applications | 2018 | 25 Pages |
Abstract
We introduce a definition of the volume of a general rectangular matrix, which is equivalent to an absolute value of the determinant for square matrices. We generalize results of square maximum-volume submatrices to the rectangular case, show a connection of the rectangular volume with an optimal experimental design and provide estimates for a growth of coefficients and an approximation error in spectral and Chebyshev norms. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
A. Mikhalev, I.V. Oseledets,