Density of diagonalizable matrices in sets of structured matrices defined from indefinite scalar products

Abstract

For an (indefinite) scalar product $[x,y{]}_B=x^{H}By$ for $B=\pm B^H\in G{l}_n(\mathbb{C})$ 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.

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