Linear Algebra | CHAPTER3 / Projection

This section is optional; only the last two sections of Chapter Five require this material.

We have described the projection $\pi$ from $\Re^3$ into its

$xy$ plane subspace as a ‘shadow map’.

This shows why, but it also shows that some shadows fall upward.

So perhaps a better description is: the projection of $\vec{v}$ is the

$\vec{p}$ in the plane with the property that someone standing on

$\vec{p}$ and looking straight up or down sees $\vec{v}$ . In this

section we will generalize this to other projections, both orthogonal (i.e., ‘straight up and down’) and nonorthogonal.