Fundamental Subspaces

If we are given a matrix . It has fundamental subspaces:

These subspaces are really the subspaces associated with the linear transformation defined by . So the matrix doesn't contain these subspaces, it creates them when acting on vectors.

Properties

The fundamental subspaces can be related as follows:

This means that:

Example:

Go to Finding Fundamental Subspaces to see a worked example of finding the fundamental subspaces given a matrix .