Article
| Title: | A note on eigenvalue of tensors and its application (English) |
| Author: | Nayak, Snigdhashree |
| Author: | Panigrahy, Krushnachandra |
| Author: | Mishra, Debasisha |
| Author: | Mishra, Nachiketa |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 70 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 563-594 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The tensor eigenvalue problem has been widely studied in recent years. In this paper, several new properties of eigenvalues and determinants of tensors are explored. We also proposed a formula to compute the determinant of a tensor as a mimic of the matrix determinant. The Perron-Frobenius theorem, one of the most important results in non-negative matrix theory, is proposed for the class of non-negative tensors in the Einstein product framework. Further, the power method, a widely used matrix iterative method for finding the largest eigenvalue, is framed for tensors using the Einstein product. The proposed higher-order power method is applied to calculate the largest eigenvalue of the Laplacian tensors associated with hyper-stars and hyper-trees. The numerical results show that the higher-order power method with the Einstein product is stable. (English) |
| Keyword: | eigenvalue |
| Keyword: | eigentensor |
| Keyword: | determinant |
| Keyword: | Einstein product |
| Keyword: | power method |
| MSC: | 15A18 |
| MSC: | 15A69 |
| DOI: | 10.21136/AM.2025.0022-25 |
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| Date available: | 2025-10-03T12:42:03Z |
| Last updated: | 2025-10-06 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153093 |
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