# Definition:Nullity

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## Definition

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

### Matrix

Let $\mathbf A$ be a matrix.

Then the nullity of $\mathbf A$ is defined to be the dimension of the null space of $\mathbf A$.