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Consider the system y(t)=I_n*x(t) where <math>I^n</math> is the identity matrix and y(t) and x(t) are n x 1 vectors. | Consider the system y(t)=I_n*x(t) where <math>I^n</math> is the identity matrix and y(t) and x(t) are n x 1 vectors. | ||
Revision as of 09:51, 10 September 2008
Linear System Definition
A system takes a given input and produces an output. For the system to be linear it must preserve addition and multiplication. In mathematical terms:
$ x(t+t0)=x(t) + x(t0) $
and
$ x(k*t)=k*x(t) $
Linear System Example
font=4 Consider the system y(t)=I_n*x(t) where $ I^n $ is the identity matrix and y(t) and x(t) are n x 1 vectors.
