What is a linear system?

Question

What is a linear system?

Answer 1

You can find mathematical definitions all over the web, so I won't get into that.  But the basic difference is that linear systems exhibit the properties of superposition and scaling.

What that means is that if you have two linear systems and you combine them, the resulting system can be described, mathematically, as the addition of the mathematical descriptions of the two original systems.  Non-linear systems can't do that.

Scaling refers to the input and output.  In a linear system, if you ramp up the input, the output will react in stable, generally easy-to-predict way.  By contrast, a non-linear system (such as the weather) is usually best described by probabilities.  Despite hundreds of thousands of sensors across the globe, we can't predict the weather out further than a week or so because it's a nonlinear system.  By contrast, we can predict planetary motion for several millenia because (on those timescales) it's a linear process.  [If you want to get technical, everything is non-linear because of uncertainties in the measurements and process, but most things can be described by linear processes for short periods of time or with certain constraints]

Answer 2

It is either a system of linear equations like this

http://en.wikipedia.org/wiki/System_of_l...

or a mathematical model that uses linear operator like this

http://en.wikipedia.org/wiki/Linear_syst...

You are asking two chapters of textbook, and I shouldn't spend time explaining when it's already published....