[math] \newcommand{\mathds}{\mathbb}[/math]

Work out what happens to the main diagonalization theorem for the matrices [math]A\in M_N(\mathbb C)[/math], in the cases [math]A\in M_2(\mathbb C)[/math], [math]A\in M_N(\mathbb R)[/math], and [math]A\in M_2(\mathbb R)[/math].