\begin{definition}[Definition:Invariant Subspace]
Let $H$ be a Hilbert space.
Let $A \in B \left({H}\right)$ be a bounded linear operator.
Let $M$ be a closed linear subspace of $H$.
Then $M$ is said to be an '''invariant subspace for $A$''' iff $h \in M \implies Ah \in M$.
That is, if $AM \subseteq M$.
\end{definition}