Complete flag
= Complete flag
{title2=$0=V_0\subset V_1\subset\cdots\subset V_n=V$}
A complete flag in an $n$-dimensional <vector space> is a nested sequence of <vector subspaces> with $\dim V_i=i$. An action preserves such a flag exactly when its <matrices> are upper triangular in a <basis> adapted to the flag. The <Lie theorem> supplies an invariant complete flag for every complex finite-dimensional <Lie algebra representation> of a <Solvable Lie algebra>.