Definition:Linear Transformation

Definition
A linear transformation is a homomorphism from one module to another.

Also known as
The term linear mapping can sometimes be found, which means the same thing as linear transformation.

Some sources use the term module homomorphism.

Some authors, specifically in the field of functional analysis, use the term linear operator (or even just operator) for arbitrary linear transformations.

Some authors use the term linear functional, especially in the field of category theory.