I need a source fornthe following statement:
If $\mathfrak{g}$ is a subalgebra of $\mathrm{Mat}_n$, an element $X$ is regular if and only if its Jordan normal form contains a single Jordan block for each eigenvalue.
I know that tbis is true for a complex $\mathfrak{g}$, but I need a source. I am also interested in that statement for a real Lie algebra (Jordan normal form still over the complex numbers).