Definition:Nullity

Of a Linear Transformation
Let $\phi$ be a linear transformation from one vector space to another.

If the kernel of $\phi$ is finite-dimensional, its dimension is called the nullity of $\phi$ and is denoted $\nu \left({\phi}\right)$.

Of a Matrix
Let $\mathbf A$ be a matrix representation of $\phi$.

Then the nullity of $\phi$ can be defined as the dimension of the null space of $\mathbf A$.