Communications in Mathematical Sciences

Volume 7 (2009)

Number 3

Multiplicity of singular values for tensors

Pages: 611 – 625

DOI: http://dx.doi.org/10.4310/CMS.2009.v7.n3.a5

Authors

K. C. Chang

Tan Zhang

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.

Keywords

Singular value; eigenvalue; tensor; Liusternik-Schnirelmann theory; category; cuplength

2010 Mathematics Subject Classification

15A18, 15A69, 55M30, 58C40

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