Definition:Index of Fredholm Operator

Definition
Let $U, V$ be vector spaces over a field $K$.

Let $T: U \to V$ be a linear transformation of finite index.

The index of $T$ is defined as:
 * $\map {\mathrm{ind} } T := \map \dim {\map \ker T} - \map {\mathrm {codim}} {\Img T}$

where $\map {\mathrm {codim}} {\Img T}$ denotes the codimension of $\Img T$ in $V$.