Lie's theorem

This fact is related to: Lie algebras
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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