Quiz 6

• (p.116) 2.14
• (p.169) 2.1(d, e, g)
  • (e)

    Let

    $U\in \mathcal{L}(V,W)$ be unitary and

    $V$,

    $W$ are inner product spaces.
    Then

    $U^{\ast }U=I_V$, that is,

    $U^{\ast }=U^{-1}$.
    Since the inverse operator is unique,

    $I_W=U{U}^{-1}=U{U}^{\ast }$.
    Therefore,

    $U^{\ast }$ is also unitary.

    We have use the lemma: unitary iff

    $U^{\ast }U=I$ and uniqueness of inverse operator.

• (p.169) 2.5-2.9

Quiz 05/22

• quiz0522