Singular Values and Eigenvalues of Tensors: A Variational Approach

2006/07/26 by Lek-Heng Lim · 2 citations
Computer Science · Mathematics · #cs.IR #cs.NA #math.NA #math.OC #math.SP #msc:15A18 #msc:15A48 #msc:15A69 #msc:15A72 #msc:65F15 #msc:65K10

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published as Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP '05), Vol. 1 (2005), pp. 129--132

arxiv created 2006/07/26 · arxiv updated 2009/12/01

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.

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