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| + | Consider the system \mathbf{x}\mathbf{M}=\mathbf{b} where <math>I^n</math> is the identity matrix and y(t) and x(t) are n x 1 vectors. | ||
Revision as of 09:53, 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
Consider the system \mathbf{x}\mathbf{M}=\mathbf{b} where $ I^n $ is the identity matrix and y(t) and x(t) are n x 1 vectors.
