The solution of the Loewy–Radwan conjecture

Omladič, Matjaž (avtor), Šivic, Klemen (avtor)

A seminal result of Gerstenhaber gives the maximal dimension of a linear space of nilpotent matrices. It also exhibits the structure of such a space when the maximal dimension is attained. Extensions of this result in the direction of linear spaces of matrices with a bounded number of eigenvalues have been studied. In this paper, we answer what is perhaps the most general problem of the kind as proposed by Loewy and Radwan, by solving their conjecture in the positive. We give the maximal dimension of a vector space of $n \times n$ matrices with no more than $k < n$ eigenvalues. We also exhibit the structure of the spaces for which this dimension is attained.

• Jezik: Angleški jezik
• Ključne besede: linear space of matrices, eigenvalues, maximal number of distinct eigenvalues, dimension, structure, representation of groups
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2024
• Št. strani: Str. 2592–2618
• Številčenje: Vol. 72, no. 15
• PID: 20.500.12556/RUL-163046
• UDK: 512
• ISSN pri članku: 0308-1087
• DOI: 10.1080/03081087.2023.2277207
• COBISS.SI-ID: 178861571
• Datum objave v RUL: 01.10.2024

Gradivo je del revije

• Naslov: Linear and multilinear algebra
• Skrajšan naslov: Linear multilinear algebra
• Založnik: Taylor & Francis
• ISSN: 0308-1087
• COBISS.SI-ID: 25872128

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.