Definition
A system in which the outputs are components of an linear eqation which is equal to the value of a linear operator applied to a linear equation whose components are the inputs.
Examples
Linear System:
Equation: $ y[n] = 54x[n] $
$ x_{1}[n] \to sys \to *a \to $ $ + \to 54a x_{1}[n] + 54b x_{2}[n] $ $ x_{2}[n] \to sys \to *b \to $
$ x_{1}[n] \to *a \to $ $ + \to sys \to 54a x_{1}[n] + 54b x_{2}[n] $ $ x_{2}[n] \to *b \to $
Non-Linear System:
Equation: $ y[n] = x[n]^4 $
$ x_{1}[n] \to sys \to *a \to $ $ + \to a x_{1}[n]^4 + b x_{2}[n]^4 $ $ x_{2}[n] \to sys \to *b \to $
$ x_{1}[n] \to *a \to $ $ + \to sys \to (a x_{1}[n] + b x_{2}[n])^4 $ $ x_{2}[n] \to *b \to $
