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

Flavien Mabilat

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arXiv · 2308.15845

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

Flavien Mabilat

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Abstract

In this note, we consider matrices similar to $X$-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 $X$-form matrices over $\mathbb{R}$ and $\mathbb{C}$ are dense and we give a characterization of the interior of this set.

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Flavien Mabilat. 2023-08-30. A dense subset of $M\_{n}(\mathbb{R})$ containing diagonalizable matrices. https://arxiv.org/abs/2308.15845

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