Linear Map

Definition

$f:V\to W$

A mapping between two vector spaces that preserves Additivity on a vector addition $(V,+)$ and Homogeneity on a scalar multiplication $(F,\cdot )$ on $V$

• Additivity: $f(\mathbf{u}+\mathbf{v})=f(\mathbf{u})+f(\mathbf{v})$
• Homogeneity: $f(c\mathbf{u})=cf(\mathbf{u})$