## A multilinear singular value decomposition (2000)

Venue: | SIAM J. Matrix Anal. Appl |

Citations: | 232 - 13 self |

### BibTeX

@ARTICLE{Lathauwer00amultilinear,

author = {Lieven De Lathauwer and Bart De Moor and Joos Vandewalle},

title = {A multilinear singular value decomposition},

journal = {SIAM J. Matrix Anal. Appl},

year = {2000},

volume = {21},

pages = {1253--1278}

}

### Years of Citing Articles

### OpenURL

### Abstract

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.