Ado's theorem

Statement
Suppose $$K$$ is a field of characteristic equal to zero and $$L$$ is a finite-dimensional Lie algebra over $$K$$. Then, $$L$$ can be embedded as a subalgebra of the Lie algebra $$\mathfrak{g}\mathfrak{l}(n,K)$$ for some finite $$n$$. This algebra is just the matrix algebra $$M(n,K)$$ where the Lie bracket is defined as the additive commutator $$[X,Y] = XY - YX$$.

In particular, this result applies to the field of real numbers $$\R$$ and the field of complex numbers $$\mathbb{C}$$.