Exercise 4.2.10

Answers

P_{2} = \frac{a_{2} a_{2}^{T}}{a_{2}^{T} a_{2}} = [\begin{matrix} 0.2 & 0.4 \\ 0.4 & 0.8 \end{matrix}],

P_{2} a_{1} = [\begin{matrix} 0.2 \\ 0.4 \end{matrix}],

P_{1} = \frac{a_{1} a_{1}^{T}}{a_{1}^{T} a_{1}} = [\begin{matrix} 1 & 0 \\ 0 & 0 \end{matrix}],

P_{1} P_{2} a_{1} = [\begin{matrix} 0.2 \\ 0 \end{matrix}] .

This is not $a_{1} = (1, 0)$ . No, $P_{1} P_{2} \neq {(P_{1} P_{2})}^{2}$ .

mathchakra

2023-09-14 07:26