On the dimension of affine subspaces of nilpotent matrices

2025/08/08 by Simone Calamai, Calamai, Simone, Elena Rubei +1
Computer Science · Mathematics · #15A30 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2508.06653

openalex publication_date 2025/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• On affine spaces of rectangular matrices with constant rank
• On affine spaces of alternating matrices with constant rank
• Maximal dimension of affine subspaces of specific matrices
• The structured Gerstenhaber problem (II)
• On symmetric degeneracy loci, spaces of symmetric matrices of constant rank and dual varieties

Related

• Maximal dimension of affine subspaces of specific matrices
• On affine spaces of rectangular matrices with constant rank
• A dimension bound for constant rank subspaces of matrices over a finite field
• On affine spaces of alternating matrices with constant rank
• On the dimension of some real, bounded rank, matrix spaces