Exercise 4.4.23

Answers

You can see why

q_{1} = [\begin{matrix} 1 \\ 0 \\ 0 \end{matrix}], q_{2} = [\begin{matrix} 0 \\ 0 \\ 1 \end{matrix}], q_{3} = [\begin{matrix} 0 \\ 1 \\ 0 \end{matrix}] .

A = [\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix}] [\begin{matrix} 1 & 2 & 4 \\ 0 & 3 & 6 \\ 0 & 0 & 5 \end{matrix}] = QR .

This $Q$ is just a permutation matrix – certainly orthogonal.

mathchakra

2023-09-14 08:28