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 $

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett