Definition:Nullity

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 $\map \nu \phi$.

Matrix

Let $\mathbf A$ be a matrix.

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

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): nullity
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): null space