Definition:Nullity
Jump to navigation
Jump to search
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