Definition:Inverse Linear Operator

Definition
Let $X$ be a vector space.

Let $A : X \to X$ be an invertible (in the sense of a mapping) linear transformation with inverse mapping $A^{-1} : X \to X$.

We say that $A^{-1}$ is the inverse linear operator of $A$.

Also see

 * Inverse of Linear Operator is Linear Operator
 * Definition:Invertible Bounded Linear Operator