A video lesson proving that the projection of a vector is actually the closest vector in the subspace to the original vector.

A video lesson proving that any projection onto a subspace is actually a linear transformation. It includes a brief description of how the results can be useful in 3-D graphical programming.

A video lesson explaining the least squares approximation for otherwise unsolvable matrix equations. Presents the motivation for why the least squares approximation is useful. Derives the formula for finding the least squares approximation.

This is a video lesson on using the least squares approximation to find the line of best fit for a set of points. Includes a concrete example dealing with a set of 4 points.

This video uses a concrete example for how to find the projection of an arbitrary vector onto a specific subspace in R4. Uses a 4 x 2 basis matrix for the subspace.

A video lesson showing what a projection onto a plane could look like. Illustrates that the newly derived definition of a projection holds true for projections onto subspaces other than lines.

A video lesson figuring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.