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Geometry of Matrix Decompositions Seen Through Optimal Transport and Information Geometry

Journal article
Authors Klas Modin
Published in Journal of Geometric Mechanics
Volume 9
Issue 3
Pages 335-390
ISSN 1941-4889
Publication year 2017
Pages 335-390
Language en
Links arxiv.org/pdf/1601.01875
doi.org/10.3934/jgm.2017014
Subject categories Computational Mathematics, Geometry

Abstract

We survey classical matrix decomposition and their connection to optimal mass transport (OMT) and information geometry, emphasizing the Riemannian point-of-view. The link is obtained by considering OMT and information geometry in the category of linear transformations and multivariate Gaussian distributions. In this way, OMT is directly related to the polar decomposition of matrices, whereas information geometry is directly related to the QR, Cholesky, spectral, and singular value decompositions.

Page Manager: Webmaster|Last update: 9/11/2012
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