T-Eigenvalues of Third-Order Quaternion Tensors
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, alo...
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MDPI AG
2025-05-01
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| author | Zhuo-Heng He Mei-Ling Deng Shao-Wen Yu |
| author_facet | Zhuo-Heng He Mei-Ling Deng Shao-Wen Yu |
| author_sort | Zhuo-Heng He |
| collection | DOAJ |
| description | 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 <i>Geršgorin</i> theorem for matrices to quaternion third-order tensors. |
| format | Article |
| id | doaj-art-6a6de03109b94a00a3d1f9b45dcd0cd5 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-6a6de03109b94a00a3d1f9b45dcd0cd52025-08-20T03:47:57ZengMDPI AGMathematics2227-73902025-05-011310154910.3390/math13101549T-Eigenvalues of Third-Order Quaternion TensorsZhuo-Heng He0Mei-Ling Deng1Shao-Wen Yu2Department of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics and Newtouch Center for Mathematics, Shanghai University, Shanghai 200444, ChinaSchool of Mathematics, East China University of Science and Technology, Shanghai 200237, ChinaIn 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 <i>Geršgorin</i> theorem for matrices to quaternion third-order tensors.https://www.mdpi.com/2227-7390/13/10/1549Hermitianquaternion tensorT-eigenvalue<i>Geršgorin</i> theorem |
| spellingShingle | Zhuo-Heng He Mei-Ling Deng Shao-Wen Yu T-Eigenvalues of Third-Order Quaternion Tensors Mathematics Hermitian quaternion tensor T-eigenvalue <i>Geršgorin</i> theorem |
| title | T-Eigenvalues of Third-Order Quaternion Tensors |
| title_full | T-Eigenvalues of Third-Order Quaternion Tensors |
| title_fullStr | T-Eigenvalues of Third-Order Quaternion Tensors |
| title_full_unstemmed | T-Eigenvalues of Third-Order Quaternion Tensors |
| title_short | T-Eigenvalues of Third-Order Quaternion Tensors |
| title_sort | t eigenvalues of third order quaternion tensors |
| topic | Hermitian quaternion tensor T-eigenvalue <i>Geršgorin</i> theorem |
| url | https://www.mdpi.com/2227-7390/13/10/1549 |
| work_keys_str_mv | AT zhuohenghe teigenvaluesofthirdorderquaterniontensors AT meilingdeng teigenvaluesofthirdorderquaterniontensors AT shaowenyu teigenvaluesofthirdorderquaterniontensors |