# Linear System

A system is defined as a linear system if it has the two properties:

- Homogeneity: $h(ax)=a⋅h(x)$
- Superposition: $h(x_{1})+h(x_{2})=h(x_{1}+x_{2})$

Serendipity with Linear Transformation.

combining both: $ay_{1}(t)+by_{2}(t)=h(ax_{1}(t)+bx_{2}(t))$

Definition 5: Linearity

A system S is linear if it has the property that if f(t) and g(t) are input signals and $α,β∈C$ then $S(αf_{1}+βf_{2})=αS(f_{1})+βS(f_{2})$