Linear Algebra/Projection

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

We have described the projection $\pi$ from ${ℝ}^3$ 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 $\overrightarrow{v}$ is the $\overrightarrow{p}$ in the plane with the property that someone standing on $\overrightarrow{p}$ and looking straight up or down sees $\overrightarrow{v}$. In this section we will generalize this to other projections, both orthogonal (i.e., "straight up and down") and nonorthogonal.