Nonsingular H-tensor and its criteria
H-tensor is a new developed concept in tensor analysis and it is an extension of H-matrix and M-tensor. Based on the spectral theory of nonnegative tensors, several equivalent conditions of nonsingular H-tensors are established in the literature. However, these conditions can not be used as a criter...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
American Institute of Mathematical Sciences (A I M S Press)
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/40382 |
| _version_ | 1848755855785197568 |
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| author | Wang, Y. Zhou, Guanglu Caccetta, Louis |
| author_facet | Wang, Y. Zhou, Guanglu Caccetta, Louis |
| author_sort | Wang, Y. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | H-tensor is a new developed concept in tensor analysis and it is an extension of H-matrix and M-tensor. Based on the spectral theory of nonnegative tensors, several equivalent conditions of nonsingular H-tensors are established in the literature. However, these conditions can not be used as a criteria to identify nonsingular H-tensors as they are hard to verify. In this paper, based on the diagonal product dominance and S diagonal product dominance of a tensor, we establish some new implementable criteria in identifying nonsingular H-tensors. The positive definiteness of nonsingular H-tensors with positive diagonal entries is also discussed in this paper. The obtained results extend the corresponding conclusions for nonsingular H-matrices and improve the existing results for nonsingular H-tensors. |
| first_indexed | 2025-11-14T09:02:56Z |
| format | Journal Article |
| id | curtin-20.500.11937-40382 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:02:56Z |
| publishDate | 2016 |
| publisher | American Institute of Mathematical Sciences (A I M S Press) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-403822017-09-13T13:38:56Z Nonsingular H-tensor and its criteria Wang, Y. Zhou, Guanglu Caccetta, Louis H-tensor is a new developed concept in tensor analysis and it is an extension of H-matrix and M-tensor. Based on the spectral theory of nonnegative tensors, several equivalent conditions of nonsingular H-tensors are established in the literature. However, these conditions can not be used as a criteria to identify nonsingular H-tensors as they are hard to verify. In this paper, based on the diagonal product dominance and S diagonal product dominance of a tensor, we establish some new implementable criteria in identifying nonsingular H-tensors. The positive definiteness of nonsingular H-tensors with positive diagonal entries is also discussed in this paper. The obtained results extend the corresponding conclusions for nonsingular H-matrices and improve the existing results for nonsingular H-tensors. 2016 Journal Article http://hdl.handle.net/20.500.11937/40382 10.3934/jimo.2016.12.1173 American Institute of Mathematical Sciences (A I M S Press) unknown |
| spellingShingle | Wang, Y. Zhou, Guanglu Caccetta, Louis Nonsingular H-tensor and its criteria |
| title | Nonsingular H-tensor and its criteria |
| title_full | Nonsingular H-tensor and its criteria |
| title_fullStr | Nonsingular H-tensor and its criteria |
| title_full_unstemmed | Nonsingular H-tensor and its criteria |
| title_short | Nonsingular H-tensor and its criteria |
| title_sort | nonsingular h-tensor and its criteria |
| url | http://hdl.handle.net/20.500.11937/40382 |