Definition:Fredholm Operator

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

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

Let $\map \ker T$ denote the kernel of $T$.

Let $\Img T$ denote the image of $T$.

A $T$ is said to have finite index :


 * $\paren 1$ $\map \ker T$ is finite-dimensional.
 * $\paren 2$ The quotient space $V / \Img T$ is finite-dimensional.