# Killing form

Hi,

is there a simple possibility to calculate the Killing form in some standard matrix Lie-Algebras like $\mathfrak{so}(n,\mathbb{R})$?

With an explicit example in mind we have a fundamental representation / setting where $n\times n$ or $(2n)\times(2n)$ matrices appear explicitly, and the Killing form can be written - up to a multiplicative constant depending on $n$ - in the form $B(X,Y) = \textrm{Trace}(XY)$ .