Solution
= Solution
Let $P=|\psi\rangle\langle\psi|$. Since $|\psi\rangle$ is normalized, $P^2=P=P^\dagger$. Hence the <Householder reflection>
$$
A=I-2P
$$
is Hermitian and
$$
A^\dagger A=A^2=I-4P+4P^2=I.
$$
Therefore \b[$A$ is unitary].
= Solution
Let $P=|\psi\rangle\langle\psi|$. Since $|\psi\rangle$ is normalized, $P^2=P=P^\dagger$. Hence the <Householder reflection>
$$
A=I-2P
$$
is Hermitian and
$$
A^\dagger A=A^2=I-4P+4P^2=I.
$$
Therefore \b[$A$ is unitary].