T-Eigenvalues of Third-Order Quaternion Tensors

Zhuo-Heng He, Mei-Ling Deng and Shao-Wen Yu ()
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Zhuo-Heng He: Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China
Mei-Ling Deng: Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, China
Shao-Wen Yu: School of Mathematics, East China University of Science and Technology, Shanghai 200237, China

Mathematics, 2025, vol. 13, issue 10, 1-17

Abstract: In this paper, theories, algorithms and properties of eigenvalues of quaternion tensors via the t-product termed T-eigenvalues are explored. Firstly, we define the T-eigenvalue of quaternion tensors and provide an algorithm to compute the right T-eigenvalues and the corresponding T-eigentensors, along with an example to illustrate the efficiency of our algorithm by comparing it with other methods. We then study some inequalities related to the right T-eigenvalues of Hermitian quaternion tensors, providing upper and lower bounds for the right T-eigenvalues of the sum of a pair of Hermitian tensors. We further generalize the Weyl theorem from matrices to quaternion third-order tensors. Additionally, we explore estimations related to right T-eigenvalues, extending the Geršgorin theorem for matrices to quaternion third-order tensors.

Keywords: Hermitian; quaternion tensor; T-eigenvalue; Geršgorin theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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