# 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 $\nu \left({\phi}\right)$.