Encoding zooms (scaling) with a diagonal matrix#

If I want to express the fact that I am expanding or contracting a coordinate along the x axis, then I multiply the x coordinate by some scalar $$p$$:

$\begin{split} \begin{bmatrix} x'\\ y'\\ z'\\ \end{bmatrix} = \begin{bmatrix} p x\\ y\\ z\\ \end{bmatrix} \end{split}$

In general if I want to scale by $$p$$ in $$x$$, $$q$$ in $$y$$ and $$r$$ in $$z$$, then I could multiply each coordinate by the respective scaling:

$\begin{split} \begin{bmatrix} x'\\ y'\\ z'\\ \end{bmatrix} = \begin{bmatrix} p x\\ q y\\ r z\\ \end{bmatrix} \end{split}$

We can do the same thing by multiplying the coordinate by a matrix with the scaling factors on the diagonal:

$\begin{split} \begin{bmatrix} x'\\ y'\\ z'\\ \end{bmatrix} = \begin{bmatrix} p x\\ q y\\ r z\\ \end{bmatrix} = \begin{bmatrix} p & 0 & 0 \\ 0 & q & 0 \\ 0 & 0 & r \\ \end{bmatrix} \begin{bmatrix} x\\ y\\ z\\ \end{bmatrix} \end{split}$

You can make these zooming matrices with np.diag:

import numpy as np
zoom_mat = np.diag([3, 4, 5])
zoom_mat

array([[3, 0, 0],
[0, 4, 0],
[0, 0, 5]])