Related papers: Poset-refined majorization relations

Poset-refined majorization relations

URL: http://arxiv.org/abs/2607.28061v1
Date: Thu, 30 Jul 2026 11:40:14 GMT
Title: Poset-refined majorization relations
Abstract summary: Several classical majorization relations for sums or products of matrices involve a majorizing vector of perfectly aligned eigenvalues or singular values.<n>We show that the majorization can be strengthened, provided the change-of-basis matrices admit an LU-approximation with respect to this partial order.<n>In this way, we obtain refined versions of Ky Fan's majorization relations, Horn's log-majorization relation, and von Neumann's trace inequality.
Score: 45.88028371034407
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
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.

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