Our lives are greatly simplified by the fact that viewing transformations transform the eye to the origin and the look-at direction (optical axis) to a specified coordinate axis. This greatly reduces the range of possible projection matrices.

The projection transformation maps all of our 3-D coordinates onto our desired viewing plane. Thus, making our 3-D world into a 2-D image. This sort of mapping is not affine like all of the transforms we've discussed thus far. In fact, projection matrices do not transform points from our affine space back into the same space. They transform points into something different. Usually, we will use a projection matrix to reduce the dimensionality of our affine points.

Thus, we should expect projection matrices to be less than full rank.