Numerical range for weighted Moore-Penrose inverse of tensor
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911093344960512 |
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| author | Be, Aaisha Shekhar, Vaibhav Mishra, Debasisha |
| author_facet | Be, Aaisha Shekhar, Vaibhav Mishra, Debasisha |
| contents | This article first introduces the notion of weighted singular value decomposition (WSVD) of a tensor via the Einstein product. The WSVD is then used to compute the weighted Moore-Penrose inverse of an arbitrary-order tensor. We then define the notions of weighted normal tensor for an even-order square tensor and weighted tensor norm. Finally, we apply these to study the theory of numerical range for the weighted Moore-Penrose inverse of an even-order square tensor and exploit its several properties. We also obtain a few new results in the matrix setting that generalizes some of the existing results as particular cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_10832 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Numerical range for weighted Moore-Penrose inverse of tensor Be, Aaisha Shekhar, Vaibhav Mishra, Debasisha Numerical Analysis Functional Analysis 15A69, 15A60 This article first introduces the notion of weighted singular value decomposition (WSVD) of a tensor via the Einstein product. The WSVD is then used to compute the weighted Moore-Penrose inverse of an arbitrary-order tensor. We then define the notions of weighted normal tensor for an even-order square tensor and weighted tensor norm. Finally, we apply these to study the theory of numerical range for the weighted Moore-Penrose inverse of an even-order square tensor and exploit its several properties. We also obtain a few new results in the matrix setting that generalizes some of the existing results as particular cases. |
| title | Numerical range for weighted Moore-Penrose inverse of tensor |
| topic | Numerical Analysis Functional Analysis 15A69, 15A60 |
| url | https://arxiv.org/abs/2212.10832 |