TM-Eigenvalues of Odd-Order Tensors

doi:10.1007/s42967-021-00172-z

Communications on Applied Mathematics and Computation ›› 2022, Vol. 4 ›› Issue (4): 1258-1279.doi: 10.1007/s42967-021-00172-z

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T_M-Eigenvalues of Odd-Order Tensors

M. Pakmanesh, Hamidreza Afshin

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

Received:2021-05-07 Revised:2021-08-26 Online:2022-12-20 Published:2022-09-26

Abstract

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: T_M-product, T_M-eigenvalue, T_M-Schur form, T_M-Jordan canonical form, Oddorder tensor, F_M-upper (lower) triangular tensor

CLC Number:

M. Pakmanesh, Hamidreza Afshin. T_M-Eigenvalues of Odd-Order Tensors[J]. Communications on Applied Mathematics and Computation, 2022, 4(4): 1258-1279.

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[1]	Yun Miao, Liqun Qi, Yimin Wei. T-Jordan Canonical Form and T-Drazin Inverse Based on the T-Product [J]. Communications on Applied Mathematics and Computation, 2021, 3(2): 201-220.
[2]	Guangbin Wang, Fuping Tan. Some Criteria for H-Tensors [J]. Communications on Applied Mathematics and Computation, 2020, 2(4): 641-651.

T_M-Eigenvalues of Odd-Order Tensors

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