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arXiv · 2305.06323

On the tubular eigenvalues of third-order tensors

Fatemeh P. A. Beik·Yousef Saad
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Abstract

This paper introduces the notion of tubular eigenvalues of third-order tensors with respect to T-products of tensors and analyzes their properties. A focus of the paper is to discuss relations between tubular eigenvalues and two alternative definitions of eigenvalue for third-order tensors that are known in the literature, namely eigentuple and T-eigenvalue. In addition, it establishes a few results on tubular spectra of tensors which can be exploited to analyze the convergence of tubular versions of iterative methods for solving tensor equations.

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Fatemeh P. A. Beik, Yousef Saad. 2023-05-10. On the tubular eigenvalues of third-order tensors. https://arxiv.org/abs/2305.06323

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