Economics Dynamics Problems 233

Economics Dynamics Problems 233 - Discrete systems of...

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Discrete systems of equations 217 In each of these instructions the last line is a check that undertaking the matrix multiplication does indeed lead to the Jordan form of the matrix. In each package we get the Jordan form J = ± 10 03 ² However, the transition matrix in each package on the face of it looks different. More speciFcally, Mathematica V = ± 11 ² Maple V = ³ 1 2 1 2 1 2 1 2 ´ Butthesearefundamentallythesame.Wenotedthiswhenderivingtheeigenvectors in the previous section. We arbitrarily chose values for v r 1 or v r 2 (along with the values associated with the eigenvalue s ). In Maple , consider the Frst column, which is the Frst eigenvector. Setting v r 2 = 1, means multiplying the Frst term by 2, which gives a value for v r 1 =− 1. Similarly, setting v s 1 = 1in Maple , converts v s 2 also to the value of unity. Hence, the two matrices are identical. In each case the last instruction veriFes that V 1 AV = J .
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

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