Definition:Linear Transformation/Vector Space

Definition
Let $V, W$ be vector spaces over a field (or, more generally, division ring) $K$.

A mapping $A: V \to W$ is said to be a linear transformation :


 * $\forall v_1, v_2 \in V, \lambda \in K: A \left({\lambda v_1 + v_2}\right) = \lambda A \left({v_1}\right) + A \left({v_2}\right)$

That is, a homomorphism from one vector space to another.

Also known as
A linear transformation is also known as a linear mapping.