The problem $77.6$ from Finite Dimensional Vector Spaces:
If $A$ is a linear transformation on a real vector space $V$ and if a subspace $M$ of complexification $V^+$ is invariant under $A^+$, then $M^\perp \cap V$ is invariant under $A$.
The problem states that $M^\perp \cap V$ is invariant, but my solution proves that $M \cap V$ is.
Let $x \in M \cap V$, then $Ax = Ax + i\cdot A0 = A^+(x + i\cdot0) \in M$, by the fact that $x + i\cdot0 \in M$ and $M$ is invariant under $A^+$.
Is my proof correct?