Projection Matrix

Projection

The projection matrix is the matrix such that .

The formula for the projection matrix is as follows:

The projection matrix has the following important properties:

Projection on Subspaces

For a dimensional subspace with Orthogonal Basis we have:

This gives us the following:

Which if is an Orthonormal Basis can then be rewritten as:

The projection matrix has the following important properties:

Example

Go to Calculating Projection Matrices to see a worked example of finding the Projection Matrix given a subspace .