Geometry of Matrix Decompositions Seen Through Optimal Transport and Information Geometry
Preprint, 2015

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.

Author

Klas Modin

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Subject Categories

Computational Mathematics

Geometry

Roots

Basic sciences

More information

Created

10/7/2017