Definition:Inverse Linear Transformation

Definition
Let $V$ and $U$ be vector spaces.

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

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

Also see

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