  For an (indefinite) scalar product $[x,y]_B = x^HBy$ for $B= \pm B^H \in
Gl_n(\mathbb{C})$ on $\mathbb{C}^n \times \mathbb{C}^n$ we show that the set of
diagonalizable matrices is dense in the set of all $B$-selfadjoint,
$B$-skewadjoint, $B$-unitary and $B$-normal matrices.
