ESPM-EEP%202010%20Lecture%2026

ESPM-EEP%202010%20Lecture%2026 - ESPM 104/EEP 115 Fall...

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Unformatted text preview: ESPM 104/EEP 115 Fall 2010: Lecture 26 1. Consider the model (we will focus on 2-dimension but this applies in general to n dimensions): x ( t + 1) = A x ( t ) where x ( t ) = x 1 ( t ) x 2 ( t ) and A = a 11 a 12 a 21 a 22 2. Suppose this has eigenvalue solutions A 1 v 1 = 1 1 v 1 and A 1 v 2 = 1 1 v 2 then these two solutions can be written in matrix from as A 1 1 v 1 v 2 = 1 1 v 1 v 2 1 2 3. Define the matrices V = 1 1 v 1 v 2 and = 1 2 Then the equation in 2. can be written as AV = V AVV 1 = V V 1 A = V V 1 Note that the two equations in 2 cannot be written in matrix form as AV = V . This incorrect and does not work!...
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This note was uploaded on 02/09/2011 for the course EEP 115 taught by Professor Waynem.getz during the Fall '10 term at University of California, Berkeley.

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ESPM-EEP%202010%20Lecture%2026 - ESPM 104/EEP 115 Fall...

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