Multiplicity of singular values for tensors. (English) Zbl 1204.15020

There are many concepts and results of matrix theory that can be generalized to tensors. Among these, the authors are interested in the concepts of eigenvalue/eigenvector and singular values for tensors. However, the methods of matrix theory cannot be applied directly to the study of the eigenvalue and the singular value problems for tensors due to the nonlinear nature of the problem. In this paper the authors use critical point theory from nonlinear analysis and tools from algebraic topology to study the existence and multiplicity problem of singular values for higher order tensors.


15A18 Eigenvalues, singular values, and eigenvectors
15A69 Multilinear algebra, tensor calculus
55M30 Lyusternik-Shnirel’man category of a space, topological complexity à la Farber, topological robotics (topological aspects)
58C40 Spectral theory; eigenvalue problems on manifolds
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