\begin{definition}[Definition:Nullity/Linear Transformation]
Let $K$ be a division ring.
Let $V$ and $W$ be $K$-vector spaces.
Let $\phi: V \to W$ be a linear transformation.
Let the kernel $\ker \phi$ be finite dimensional.
Then the '''nullity of $\phi$''' is the dimension of $\ker \phi$ and is denoted $\map \nu \phi$.
\end{definition}