The eigenspace of a matrix.

We introduce the eigenspace of a matrix M. Basically, eigenspace is the span of all the eigenvectors of the matrix M.

In particular, for a matrix M of size nxn, we are interested in knowing under what conditions such a matrix would have the maximum dimension (n) for its eigenspace.

We do a few exercises on this topic also. Implicitly speaking, once again, a very good understanding of the Rank-Nullity formula (introduced in an earlier video) will help you a lot in this topic.