Linear Transformation

Definition: Linear Transformation

A linear transformation from a vector space $(V,F,+,\cdot )$ to a vector space $(W,F,+,\cdot )$ is a function $T:V\to W$ which has the property

$$T(\lambda \mathbf{u}+\mu \mathbf{v})=\lambda T(\mathbf{u})+\mu T(\mathbf{v})\forall \lambda ,\mu \in F,\forall \mathbf{u},\mathbf{v}\in V$$