Lie's theorem

This fact is related to: Lie algebras
View other facts related to Lie algebras | View terms related to Lie algebras

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