A Multilinear Singular Value Decomposition
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- 1 January 2000
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 21 (4) , 1253-1278
- https://doi.org/10.1137/s0895479896305696
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.Keywords
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