---
title: Quiz 6
tags: Linear algebra
GA: G-77TT93X4N1
---

# 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 $U^*U=I_V$, that is, $U^*=U^{-1}$.
> Since the inverse operator is unique, $I_W=UU^{-1}=UU^*$.
> Therefore, $U^*$ is also unitary.
> > We have use the [lemma: unitary iff $U^*U=I$](https://hackmd.io/@teshenglin/2024LA2_ch5_6) and [uniqueness of inverse operator](https://hackmd.io/@teshenglin/2024LA2_ch1_6).
* (p.169) 2.5-2.9

# Quiz 05/22

* [quiz0522](https://drive.google.com/file/d/1D1ulgYcxt6mkCZqMm5QsToNp26gr4UXF/view?usp=sharing)