Singular Values and Eigenvalues of Tensors: A Variational Approach
Spectral Theory
2007-05-23 v1 Information Retrieval
Numerical Analysis
Numerical Analysis
Optimization and Control
Abstract
We propose a theory of eigenvalues, eigenvectors, singular values, and singular vectors for tensors based on a constrained variational approach much like the Rayleigh quotient for symmetric matrix eigenvalues. These notions are particularly useful in generalizing certain areas where the spectral theory of matrices has traditionally played an important role. For illustration, we will discuss a multilinear generalization of the Perron-Frobenius theorem.
Cite
@article{arxiv.math/0607648,
title = {Singular Values and Eigenvalues of Tensors: A Variational Approach},
author = {Lek-Heng Lim},
journal= {arXiv preprint arXiv:math/0607648},
year = {2007}
}