(→Linear System Example) |
(→Linear System Example) |
||
| Line 12: | Line 12: | ||
| − | Consider the system <math>\mathbf{x}\mathbf{M}=\mathbf{b} </math>where <math> | + | Consider the system |
| + | <math> \mathbf{x}\mathbf{M}=\mathbf{b} </math> | ||
| + | where <math>\mathbf{M}=\begin{bmatrix} | ||
| + | 1 & 2 \\ | ||
| + | 3 & 4 \\ | ||
| + | \end{bmatrix}</math> is the identity matrix and y(t) and x(t) are n x 1 vectors. | ||
<math>Insert formula here</math> | <math>Insert formula here</math> | ||
Revision as of 09:55, 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 $ \mathbf{M}=\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ \end{bmatrix} $ is the identity matrix and y(t) and x(t) are n x 1 vectors. $ Insert formula here $
