The MPWG inverse of third-order F-square tensors based on the T-product-Reference-Cited by-同舟云学术

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The MPWG inverse of third-order F-square tensors based on the T-product

Published:2024 Issue:3 Volume:38 Page:939-956
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

He Mengyu¹,Liu Xiaoji²,Jin Hongwei¹

Affiliation:

1. School of Mathematics and Physics, Guangxi Minzu University, Nanning, China

2. School of Education, Guangxi Vocational Normal University, Nanning, China

Abstract

We define the T-MPWG inverse of third-order F-square tensors by using the T-core EP decomposition of tensors via the T-product. Then, we present some characterizations and properties of the T-MPWG inverse. Moreover, the Cayley-Hamilton theorem of the third-order tensors is extended to T-MPWG inverses. Examples are also given to illustrate these results.

Publisher

National Library of Serbia

Reference17 articles.

1. R Chan, X Jin. An introduction to iterative Toeplitz solvers. SIAM, Philadelphia, 2007.

2. Z Cong, H Ma. Characterizations and perturbations of the Core-EP inverse of tensors based on the T-Product. Numerical Functional Analysis and Optimization, 2022, 1-51.

3. D Gleich, C Greif, J Varah. The power and Arnoldi methods in an algebra of circulants. Numerical Linear Algebra with Applications, 2013, 20(5): 809-831.

4. HJin, MBai, J Benítez, XLiu. The generalized inverses of tensors and an application to linear models. Computers and Mathematics with Applications, 2017, 74(3): 385-397.

5. H Jin, W Wang, J Liu, X Liu. Further results on the generalized inverses of tensors via the T-product, submitted.

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