Communications on Applied Mathematics and Computation >

2022 , Vol. 4 >Issue 4: 1258 - 1279

DOI: https://doi.org/10.1007/s42967-021-00172-z

TM-Eigenvalues of Odd-Order Tensors

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  • Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran

Received date: 2021-05-07

  Revised date: 2021-08-26

  Online published: 2022-09-26

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Abstract

In this paper, we propose a definition for eigenvalues of odd-order tensors based on some operators. Also, we define the Schur form and the Jordan canonical form of such tensors, and discuss commuting families of tensors. Furthermore, we prove some eigenvalue inequalities for Hermitian tensors. Finally, we introduce characteristic polynomials of odd-order tensors.

Key words： TM-product; TM-eigenvalue; TM-Schur form; TM-Jordan canonical form; Oddorder tensor; FM-upper (lower) triangular tensor

Cite this article

M. Pakmanesh, Hamidreza Afshin . TM-Eigenvalues of Odd-Order Tensors[J]. Communications on Applied Mathematics and Computation, 2022 , 4(4) : 1258 -1279 . DOI: 10.1007/s42967-021-00172-z

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