Transform Invariant

A subspace that is sent to itself by the linear transform.

Definition

1. For Linear Transform $T:V\to W$
2. For a Subspace $U\subset V$
3. $U$ is $T$ invariant $⟺\forall v\in U,T(v)\in U$ Or:
4. $U$ is $T$ invariant $⟺Img(T)\subset U$ Or:
5. $\beta =\{b_1,\dots ,b_n\}$ is a basis of $U$
6. $T(b_1),\dots ,T(b_k)\in U⟹U$ is $T$ invariant