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Lecture 10: Poles and Eigenvalues

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Schedule :: Perspective :: Transfer Functions :: Laplace Transform :: Poles and Eigenvalues :: Time Domain :: Linear Transformations :: Special Transformation :: Controllability :: Discrete-Time

Recall:

\begin{displaymath}X^{-1} = \frac{\adj(X)}{\det(X)}
\end{displaymath}

Without worrying about what the adj is, note that the denominator always has the determinant. Thus

\begin{displaymath}(sI-A)^{-1} = \frac{\adj(sI-A)}{\det(sI-A)}.
\end{displaymath}

So the denominator has poles where the eigenvalues of $A$ are!
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 08). Lecture 10: Poles and Eigenvalues. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/10_4node4.html. This work is licensed under a Creative Commons License Creative Commons License