Linear Algebra/Projection

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

We have described the projection $\pi$ from $\mathbb {R} ^{3}$ 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.