To use Definition 2.7 to check whether a subspace is t invariant, we seemingly have to check

Question:

To use Definition 2.7 to check whether a subspace is t invariant, we seemingly have to check all of the infinitely many vectors in a (nontrivial) subspace to see if they satisfy the condition. Prove that a subspace is t invariant if and only if its sub basis has the property that for all of its elements, t(→β ) is in the subspace.