Communications in Mathematical Sciences

Multiplicity of singular values for tensors

K. C. Chang and Tan Zhang

Full-text: Open access

Abstract

In linear algebra, both eigenvalue problems and singular value problems for matrices are of fundamental importance. In this paper, we use critical point theory from nonlinear analysis and tools from algebraic topology to study the existence and multiplicity problem of singular values in the higher order tensor setting.

Article information

Source
Commun. Math. Sci., Volume 7, Number 3 (2009), 611-625.

Dates
First available in Project Euclid: 26 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.cms/1256562815

Mathematical Reviews number (MathSciNet)
MR2569025

Zentralblatt MATH identifier
1204.15020

Subjects
Primary: 15A18: Eigenvalues, singular values, and eigenvectors 15A69: Multilinear algebra, tensor products 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirelʹman) category of a space 58C40: Spectral theory; eigenvalue problems [See also 47J10, 58E07]

Keywords
Singular value eigenvalue tensor Liusternik-Schnirelmann theory category cuplength

Citation

Chang, K. C.; Zhang, Tan. Multiplicity of singular values for tensors. Commun. Math. Sci. 7 (2009), no. 3, 611--625. https://projecteuclid.org/euclid.cms/1256562815


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