# Linear Algebra/Projection

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.