Definition:Fredholm Operator

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

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

$T$ 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

where:
 * $\map \ker T$ denotes the kernel of $T$
 * $\Img T$ denotes the image of $T$

Also see

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