Exercise 4.2.7

Answers

P_{1} + P_{2} + P_{3} = \frac{1}{9} [\begin{matrix} 1 & - 2 & - 2 \\ - 2 & 4 & 4 \\ - 2 & 4 & 4 \end{matrix}] + \frac{1}{9} [\begin{matrix} 4 & 4 & - 2 \\ 4 & 4 & - 2 \\ - 2 & - 2 & 1 \end{matrix}] + \frac{1}{9} [\begin{matrix} 4 & - 2 & 4 \\ - 2 & 1 & - 2 \\ 4 & - 2 & 4 \end{matrix}] = I .

We can add projections onto orthogonal vectors to get the projection matrix onto the larger space. This is important.

mathchakra

2023-09-14 07:23