A Multilinear Singular Value Decomposition

Authors:
Lieven De Lathauwer;Bart De Moor;Joos Vandewalle
Affiliations:
-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2000

Citing 0
Cited 243

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Abstract

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.