  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.
