= Flag
{disambiguate=linear algebra}
{title2=$0=V_0\subset V_1\subset\cdots\subset V_r=V$}
{wiki}
= Flag of a vector space
{synonym}
A flag is a strictly nested chain of <vector subspaces> of a fixed <vector space>. A <complete flag> contains a subspace of every possible dimension. For an action by <linear maps>, an invariant flag means that each of its <vector subspaces> is an <invariant subspace>. A <basis> adapted to an invariant complete flag makes all these maps upper triangular, connecting <complete flags> to <simultaneous triangularization of a Lie algebra representation>.
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