SIAM Journal on Matrix Analysis and Applications


SIAM J. Matrix Anal. Appl., 21(4), 1253–1278. (26 pages)

A Multilinear Singular Value Decomposition

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Article Data

History

Published online: 31 July 2006

AMS Subject Headings

15A18, 15A69

Publication Data

ISSN (print): 0895-4798
ISSN (online): 1095-7162
Publisher: Society for Industrial and Applied Mathematics
CODEN: sjmael
Lieven De Lathauwer, Bart De Moor, and Joos Vandewalle
https://doi.org/10.1137/S0895479896305696

We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pair-wise symmetric tensors.

Copyright © 2000 Society for Industrial and Applied Mathematics
Permalink: https://doi.org/10.1137/S0895479896305696

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