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 $\mathbb {R}$ and the field of complex numbers $\mathbb {C}$.