Linear Map

Definition

A function $f$ between vector spaces $V$ and $W$ over a field $F$ is a linear map iff

$$\begin{array}{rl}& f({\lambda }_1\cdot v_1{+}_V{\lambda }_2\cdot v_2)={\lambda }_1\cdot (f{v}_1){+}_W{\lambda }_2\cdot (f{v}_2)\\ & (\forall v_1,v_2\in V;{\lambda }_1,{\lambda }_2\in F)\end{array}$$

References

pinter2010-abstract-algebra (ch28)