English

On the dimension of affine subspaces of nilpotent matrices

Rings and Algebras 2025-08-27 v2

Abstract

The focus of the paper is on the maximal dimension of affine subspaces of nilpotent n×nn \times n matrices with fixed rank. In particular we obtain two results in the "border" cases rank equal to n1n-1 and rank equal to 11.

Keywords

Cite

@article{arxiv.2508.06653,
  title  = {On the dimension of affine subspaces of nilpotent matrices},
  author = {Simone Calamai and Elena Rubei},
  journal= {arXiv preprint arXiv:2508.06653},
  year   = {2025}
}

Comments

15 pages; with respect to the first version we weakened the assumption on the field in Theorem 1.4