Revision as of 17:49, 10 September 2008 by Vhsieh (Talk)

Linear system

A linear system is a system that will produce the same output for both of the following actions:


1. One puts signals through the system, multiplies the outcomes by a constant, and add the results together. 2. One multiplies the same signals by the same constants, adds the results together, and sends that outcome through the system.


An example of a linear system is as follows:


$ y(t) = 15x(t)\! $


The proof for this is rather simple. Suppose you put $ x(t) = t + 12\! $ and end up with $ 15t + 180\! $. You also send $ z(t) = t - 2\pi\! $ through the system and get $ 15t - 30\pi\! $. You multiply the first outcome by $ 2\! $ and get $ 30t + 360\! $. You multiply the second result by $ 3\! $ and you get $ 45t - 90\pi\! $. After summing the two, you get $ 75t + 360 - 90\pi\! $.

Alumni Liaison

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

Dr. Paul Garrett