English

A dense subset of $M\_{n}(\mathbb{R})$ containing diagonalizable matrices

Rings and Algebras 2023-08-31 v1

Abstract

In this note, we consider matrices similar to XX-form matrices, which are the matrices for which only the diagonal and the anti-diagonal elements can be different from zero. First, we give a characterization of these matrices using the minimal polynomial. Then, we prove that the set of matrices similar to XX-form matrices over R\mathbb{R} and C\mathbb{C} are dense and we give a characterization of the interior of this set.

Keywords

Cite

@article{arxiv.2308.15845,
  title  = {A dense subset of $M\_{n}(\mathbb{R})$ containing diagonalizable matrices},
  author = {Flavien Mabilat},
  journal= {arXiv preprint arXiv:2308.15845},
  year   = {2023}
}
R2 v1 2026-06-28T12:08:09.525Z