Poset-refined majorization relations

Abstract:Several classical majorization relations for sums or products of matrices involve a majorizing vector of perfectly aligned eigenvalues or singular values. By relaxing the order of alignment to a partial order, we show that the majorization can be strengthened, provided the change-of-basis matrices admit an LU-approximation with respect to this partial order. In this way, we obtain refined versions of Ky Fan's majorization relations, Horn's log-majorization relation, and von Neumann's trace inequality. As an application, we give a short proof of the separable Ky Fan majorization relation for an arbitrary number of tensor factors and extend it to a sum of tensor products of arbitrary matrices. Further applications concern majorization relations for sums of (anti-)symmetric powers and for products of Kronecker sums.

Functional Analysis (math.FA); Quantum Physics (quant-ph)

arXiv:2607.28061 [math.FA]

(or arXiv:2607.28061v1 [math.FA] for this version)

https://doi.org/10.48550/arXiv.2607.28061 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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