Article Dans Une Revue Linear Algebra and its Applications Année : 2025

Generalized unistochastic matrices

Résumé

We study a class of bistochastic matrices generalizing unistochastic matrices. Given a complex bipartite unitary operator, we construct a bistochastic matrix having as entries the normalized squares of Frobenius norm of the blocks. We show that the closure of the set of generalized unistochastic matrices is the whole Birkhoff polytope. We characterize the points on the edges of the Birkhoff polytope that belong to a given level of our family of sets, proving that the different (non-convex) levels have a rich inclusion structure. We also study the corresponding generalization of orthostochastic matrices. Finally, we introduce and study the natural probability measures induced on our sets by the Haar measure of the unitary group. These probability measures interpolate between the natural measure on the set of unistochastic matrices and the Dirac measure supported on the van der Waerden matrix.

Dates et versions

hal-05129725 , version 1 (25-06-2025)

Identifiants

Citer

Ion Nechita, Zikun Ouyang, Anna Szczepanek. Generalized unistochastic matrices. Linear Algebra and its Applications, 2025, 721, pp.339-365. ⟨10.1016/j.laa.2024.05.019⟩. ⟨hal-05129725⟩
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