Exercise 4.4.9

(a) $Q=\left[\begin{array}{cc}\hfill .8& \hfill -.6\\ \hfill .6& \hfill .8\\ \hfill 0& \hfill 0\end{array}\right]$ has $P=Q{Q}^T=\left[\begin{array}{ccc}1\hfill & 0\hfill & 0\hfill \\ 0\hfill & 1\hfill & 0\hfill \\ 0\hfill & 0\hfill & 0\hfill \end{array}\right]=$projection on the $\mathit{xy}$ plane.

(b) $\left(Q{Q}^T\right)\left(Q{Q}^T\right)=Q\left(Q^{T}Q\right)Q^T=Q{Q}^T$.