Spectral Bounds for Tensors Derived from Trace Functionals and Wasserstein Distance in Tensor Spaces

Fuente: arXiv
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Autori principali: Sharma, Hemant, Mishra, Nachiketa
Natura: Preprint
Pubblicazione: 2026
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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