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.

翻译：本文引入张量T积意义下三阶张量的管状特征值概念，并分析其性质。论文重点探讨了管状特征值与文献中已知的两种三阶张量特征值定义（即特征组与T-特征值）之间的关系。此外，本文建立了若干关于张量管状谱的结果，这些结果可用于分析求解张量方程的迭代方法之管状版本的收敛性。