Elena Rubei

collaborators

6 papers

math.RA2025

On the dimension of affine subspaces of nilpotent matrices

Simone Calamai, Elena Rubei

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…

math.RA2024

Affine subspaces of antisymmetric matrices with constant rank

Elena Rubei

For every $n \in N$ and every field $K$ , let $A (n, K)$ be the vector space of the antisymmetric $(n \times n)$ -matrices over $K$ . We say that an affine subspace $S$ of $A(n…

math.RA2024

Affine subspace of matrices with constant rank

Elena Rubei

For every $m, n \in N$ and every field $K$ , let $M (m \times n, K)$ be the vector space of the $(m \times n)$ -matrices over $K$ and let $S (n, K)$ be the vector space of the s…

math.RA2024

Interval matrices: realization of ranks by rational matrices

Elena Rubei

Let $I^\pm$ be a $p \times q$ interval matrix with $p \geq q$ and with the endpoints of all its entries in the set of the rational numbers. We prove that, if $I^\pm$ contains a rank- $r$ …

math.RA2024

A generalization of Rohn's theorem on full-rank interval matrices

Elena Rubei

A general closed interval matrix is a matrix whose entries are closed connected nonempty subsets of the set of the real numbers, while an interval matrix is defined to be a matrix…

math.RA2024

Affine subspaces of matrices with rank in a range

Elena Rubei

The problem of finding the maximal dimension of linear or affine subspaces of matrices whose rank is constant, or bounded below, or bounded above, has attracted many mathematicians…