Chapter 74

Chapter 7 Exercise D
1. Solution. A quick calculation shows that $T^*Tv = ||x||^2\langle v, u \rangle u$ for every $v \in...
Chapter 7 Exercise C
1. Solution: We give a counterexample. Define $T \in \mathcal{L}(\mathcal{R}^2)$ by $$ \begin{aligne...
Chapter 7 Exercise B
1. Solution: It is true. Consider the standard orthonormal basis $e_1,e_2,e_3$ of $\mb R^3$. Define ...
Chapter 7 Exercise A
1. Solution: By definition, we have \[\begin{align*}\langle (z_1,\cdots,z_n),T^*(w_1,\cdots,w_n)\ran...