An eigenvalue problem for even order tensors with its applications

2015/08/06 by Lu-Bin Cui, Lu‐Bin Cui, Chuan Chen +2 · 2 citations
Mathematics · Medicine · Engineering · #Tensor decomposition and applications #Advanced Neuroimaging Techniques and Applications #Elasticity and Material Modeling

paper · doi:10.1080/03081087.2015.1071311

Abstract

In this paper, we study an eigenvalue problem for even order tensors. Using the matrix unfolding of even order tensors, we can establish the relationship between a tensor eigenvalue problem and a multilevel matrix eigenvalue problem. By considering a higher order singular value decomposition of a tensor, we show that higher order singular values are the square root of the eigenvalues of the product of the tensor and its conjugate transpose. This result is similar to that in matrix case. Also we study an eigenvalue problem for Toeplitz/circulant tensors, and give the lower and upper bounds of eigenvalues of Toeplitz tensors. An application in image restoration is also discussed.

Cited by

• A tensor phase theory with applications in multilinear control
• Hanson-Wright Inequality for Random Tensors under Einstein Product

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