Spectral Bounds for Tensors Derived from Trace Functionals and Wasserstein Distance in Tensor Spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917503174705152 |
|---|---|
| author | Sharma, Hemant Mishra, Nachiketa |
| author_facet | Sharma, Hemant Mishra, Nachiketa |
| contents | This article introduces a trace-based metric on the space of positive semi-definite (PSD) tensors, offering a geometric perspective that connects their algebraic structure to their intrinsic geometric properties. It defines the Bures-Wasserstein distance on tensor spaces, establishing clear measurements between tensors. Moreover, the study derives trace-based eigenvalue bounds for PSD tensors and analyzes how these bounds depend on the PSD condition. The behavior of these bounds is further explored when the PSD requirement is relaxed, with illustrative examples provided to support the theoretical findings. In addition, a detailed complexity analysis is carried out for the methods proposed in this study. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16930 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral Bounds for Tensors Derived from Trace Functionals and Wasserstein Distance in Tensor Spaces Sharma, Hemant Mishra, Nachiketa Numerical Analysis 15A69, 15A15, 15A18 This article introduces a trace-based metric on the space of positive semi-definite (PSD) tensors, offering a geometric perspective that connects their algebraic structure to their intrinsic geometric properties. It defines the Bures-Wasserstein distance on tensor spaces, establishing clear measurements between tensors. Moreover, the study derives trace-based eigenvalue bounds for PSD tensors and analyzes how these bounds depend on the PSD condition. The behavior of these bounds is further explored when the PSD requirement is relaxed, with illustrative examples provided to support the theoretical findings. In addition, a detailed complexity analysis is carried out for the methods proposed in this study. |
| title | Spectral Bounds for Tensors Derived from Trace Functionals and Wasserstein Distance in Tensor Spaces |
| topic | Numerical Analysis 15A69, 15A15, 15A18 |
| url | https://arxiv.org/abs/2605.16930 |