What is the difference, if any, between kernel and null space?
I previously understood the kernel to be of a linear map and the null space to be of a matrix: i.e., for any linear map $f : V \to W$,
$ \ker(f) \cong \operatorname{null}(A), $
where
- $\cong$ represents isomorphism with respect to $+$ and $\cdot$, and
- $A$ is the matrix of $f$ with respect to some source and target bases.
However, I took a class with a professor last year who used $\ker$ on matrices. Was that just an abuse of notation or have I had things mixed up all along?