Exercise 4.3.9

Answers

Parabola. Project $b$ 4D to 3D:

[\begin{matrix} 1 & 0 & 0 \\ 1 & 1 & 1 \\ 1 & 3 & 9 \\ 1 & 4 & 16 \end{matrix}] [\begin{matrix} C \\ D \\ E \end{matrix}] = [\begin{matrix} 0 \\ 8 \\ 8 \\ 20 \end{matrix}] .

A^{T} A \hat{x} = [\begin{matrix} 4 & 8 & 26 \\ 8 & 26 & 92 \\ 26 & 92 & 338 \end{matrix}] [\begin{matrix} C \\ D \\ E \end{matrix}] = [\begin{matrix} 36 \\ 112 \\ 400 \end{matrix}] .

Figure 4.9 (a) is fitting 4 points and 4.9 (b) is a projection in $R^{4}$ : same problem !

mathchakra

2023-09-14 08:06