Invariant Subspace - Invariant-subspace Lattice

Given a nonempty Σ ⊂ L(V), the invariant subspaces invariant under each element of Σ form a lattice, sometimes called the invariant-subspace lattice of Σ and denoted by Lat(Σ).

The lattice operations are defined in a natural way: for Σ' ⊂ Σ, the meet operation is defined by

while the join operation is

A minimal element in Lat(Σ) in said to be a minimal invariant subspace.