20.500.12556/RUL-163046 The solution of the Loewy–Radwan conjecture 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. linear space of matrices eigenvalues maximal number of distinct eigenvalues dimension structure representation of groups true false true Angleški jezik Ni določen Članek v reviji 2024-10-01 11:05:01 2024-10-01 11:05:04 2024-10-06 03:34:47 0000-00-00 00:00:00 2024 0 0 Str. 2592–2618 no. 15 Vol. 72 2024 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512 0308-1087 10.1080/03081087.2023.2277207 178861571 The_solution_of_the_Loewy_Radwan_conjecture.pdf The_solution_of_the_Loewy_Radwan_conjecture.pdf 1 E69A7B55E3394DEE0423D26943A2516C 6cd1b58777fe615bdbfd640c0e345b36224cfca07d4ddce5b5231583b337bf3f 57f3d9aa-7fd4-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=192513 https://www.tandfonline.com/doi/full/10.1080/03081087.2023.2277207 1 1a603f8d-7fd4-11ef-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=192512 Fakulteta za matematiko in fiziko 0 0 0