The focus of the paper is on the maximal dimension of affine subspaces of nilpotent n x n matrices with fixed rank. In particular we obtain a result in the "border" case rank equal to n-1; we also consider the much simpler case rank equal to 1.
On the dimension of affine subspaces of nilpotent matrices / Simone Calamai, Elena Rubei. - In: LINEAR ALGEBRA AND ITS APPLICATIONS. - ISSN 0024-3795. - STAMPA. - 752C:(In corso di stampa), pp. 152-170. [10.1016/j.laa.2026.08.015]
On the dimension of affine subspaces of nilpotent matrices
Simone Calamai;Elena Rubei
In corso di stampa
Abstract
The focus of the paper is on the maximal dimension of affine subspaces of nilpotent n x n matrices with fixed rank. In particular we obtain a result in the "border" case rank equal to n-1; we also consider the much simpler case rank equal to 1.
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