New results on the doubly stochastic inverse eigenvalue problem [r-libre/4184]

Bouthat, Ludovick, Mashreghi, Javad et Morneau-Guérin, Frédéric ORCID: https://orcid.org/0000-0001-7610-4648 (21 mai 2026). New results on the doubly stochastic inverse eigenvalue problem. Communication (sur invitation) présentée à la 27th Conference of the International Linear Algebra Society, Blacksburg, Virginia, États-Unis.

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Catégorie de document :	Communications à des congrès/colloques et conférences (non publiées)
Évaluation par un comité de lecture :	Non
Étape de publication :	Non publié
Résumé :	Stochastic matrices are matrices with nonnegative entries whose rows each sum to 1. When a matrix and its transpose are both stochastic, it is said to be \\emph{doubly stochastic}. In 1938, Kolmogorov proposed the problem of characterizing the region of possible eigenvalues of an n by n stochastic matrix, and Karpelevich gave a complete description thirteen years later. This talk concerns the doubly stochastic analogue: characterizing the region ωn of eigenvalues of n by n doubly stochastic matrices, which is contained in the unit disk. Perfect and Mirsky (1965) conjectured that omega_n is the union of the regions Pi_k (the convex hulls of the k-th roots of unity) for k = 1,...,n. This conjecture holds for n = 1,2,3,4, but fails for n = 5. The case n greater or equal to 6 remains open. In response to the scarcity of progress over the past 60 years, Levick, Pereira, and Kribs proposed a related conjecture. In this talk, we propose an approach to a stronger version of this conjecture. The approach, based on majorization theory and geometric properties, also provides a potential general framework for characterizing omega_5, as well as a numerical method for testing the conjecture for various values of n.
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	11 aout 2026 18:19
Dernière modification :	11 aout 2026 18:19

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