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:
 * $\map \dim {\map \ker T}$ denotes the dimension of the kernel
 * $\map {\mathrm {codim}} {\Img T}$ denotes the codimension of image in $V$

Also see

 * Linear Transformation has Finite Index iff Pseudoinverse exists
 * Definition:Pseudoinverse of Linear Transformation