Lie's theorem

Statement
Let $$V$$ be a vector space over $$\mathbb{C}$$ (or more generally, any algebraically closed field of characteristic zero). Suppose $$L$$ is a solvable Lie subalgebra of $$gl(V)$$. Then, there is a basis for $$V$$ in which all the elements of $$L$$ are represented by upper triangular matrices.

Related results

 * Engel's theorem