On the largest eigenvalue of a symmetric nonnegative tensor
In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (resp...
| Main Authors: | , , |
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| Format: | Journal Article |
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John Wiley & Sons Ltd
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/25034 |
| _version_ | 1848751594792812544 |
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| author | Zhou, Guanglu Qi, L. Wu, S. |
| author_facet | Zhou, Guanglu Qi, L. Wu, S. |
| author_sort | Zhou, Guanglu |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenvalue–eigenvector; (iii) the minimax theorem is satisfied without requiring the weak irreducibility condition; and (iv) if it is weakly reducible, then it can be decomposed into some weakly irreducible tensors. In addition, the problem of finding the largest eigenvalue of a symmetric nonnegative tensor is shown to be equivalent to finding the global solution of a convex optimization problem. Subsequently, algorithmic aspects for computing the largest eigenvalue of symmetric nonnegative tensors are discussed. |
| first_indexed | 2025-11-14T07:55:13Z |
| format | Journal Article |
| id | curtin-20.500.11937-25034 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:55:13Z |
| publishDate | 2013 |
| publisher | John Wiley & Sons Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-250342018-03-29T09:08:50Z On the largest eigenvalue of a symmetric nonnegative tensor Zhou, Guanglu Qi, L. Wu, S. eigenvalue convex optimization convergence algorithm symmetric tensor In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenvalue–eigenvector; (iii) the minimax theorem is satisfied without requiring the weak irreducibility condition; and (iv) if it is weakly reducible, then it can be decomposed into some weakly irreducible tensors. In addition, the problem of finding the largest eigenvalue of a symmetric nonnegative tensor is shown to be equivalent to finding the global solution of a convex optimization problem. Subsequently, algorithmic aspects for computing the largest eigenvalue of symmetric nonnegative tensors are discussed. 2013 Journal Article http://hdl.handle.net/20.500.11937/25034 10.1002/nla.1885 John Wiley & Sons Ltd restricted |
| spellingShingle | eigenvalue convex optimization convergence algorithm symmetric tensor Zhou, Guanglu Qi, L. Wu, S. On the largest eigenvalue of a symmetric nonnegative tensor |
| title | On the largest eigenvalue of a symmetric nonnegative tensor |
| title_full | On the largest eigenvalue of a symmetric nonnegative tensor |
| title_fullStr | On the largest eigenvalue of a symmetric nonnegative tensor |
| title_full_unstemmed | On the largest eigenvalue of a symmetric nonnegative tensor |
| title_short | On the largest eigenvalue of a symmetric nonnegative tensor |
| title_sort | on the largest eigenvalue of a symmetric nonnegative tensor |
| topic | eigenvalue convex optimization convergence algorithm symmetric tensor |
| url | http://hdl.handle.net/20.500.11937/25034 |