An extension of the Moore-Penrose Inverse of a Tensor via the Einstein product
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866915429096620032 |
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| author | Panigrahy, Krushnachandra Mishra, Debasisha |
| author_facet | Panigrahy, Krushnachandra Mishra, Debasisha |
| contents | In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a tensor called product Moore-Penrose inverse. A necessary and sufficient condition for the coincidence of the Moore-Penrose inverse and the product Moore-Penrose inverse is also proposed. Finally, the triple reverse order law of tensors is introduced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_03655 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An extension of the Moore-Penrose Inverse of a Tensor via the Einstein product Panigrahy, Krushnachandra Mishra, Debasisha Rings and Algebras In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a tensor called product Moore-Penrose inverse. A necessary and sufficient condition for the coincidence of the Moore-Penrose inverse and the product Moore-Penrose inverse is also proposed. Finally, the triple reverse order law of tensors is introduced. |
| title | An extension of the Moore-Penrose Inverse of a Tensor via the Einstein product |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/1806.03655 |