Definition:Nullity/Linear Transformation

Definition
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 $\map \nu \phi$.