The focus of the paper is on the maximal dimension of affine subspaces of nilpotent $n \times n $ matrices with fixed rank. In particular we obtain two results in the "border" cases rank equal to $n-1$ and rank equal to $1$.
On the dimension of affine subspaces of nilpotent matrices / Simone Calamai; Elena Rubei. - ELETTRONICO. - (2025), pp. 1-15.
On the dimension of affine subspaces of nilpotent matrices
Simone Calamai;Elena Rubei
2025
Abstract
The focus of the paper is on the maximal dimension of affine subspaces of nilpotent $n \times n $ matrices with fixed rank. In particular we obtain two results in the "border" cases rank equal to $n-1$ and rank equal to $1$.
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