A Spectral Theory for Tensors
Abstract
In this paper we propose a general spectral theory for tensors. Our proposed factorization decomposes a tensor into a product of orthogonal and scaling tensors. At the same time, our factorization yields an expansion of a tensor as a summation of outer products of lower order tensors . Our proposed factorization shows the relationship between the eigen-objects and the generalised characteristic polynomials. Our framework is based on a consistent multilinear algebra which explains how to generalise the notion of matrix hermicity, matrix transpose, and most importantly the notion of orthogonality. Our proposed factorization for a tensor in terms of lower order tensors can be recursively applied so as to naturally induces a spectral hierarchy for tensors.
Cite
@article{arxiv.1008.2923,
title = {A Spectral Theory for Tensors},
author = {Edinah K. Gnang and Ahmed Elgammal and Vladimir Retakh},
journal= {arXiv preprint arXiv:1008.2923},
year = {2012}
}
Comments
The paper is an updated version of an earlier version