Economics Dynamics Problems 232

Economics Dynamics Problems 232 - 216 Economic Dynamics In...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
216 Economic Dynamics In this instance the output in both programmes is almost identical. Mathematica , however, qualifes the solution For z[t] by adding 15 If[t==0,1,0] .IF t is time, then this will not occur, and so this conditional statement can be ignored, in which case the two programmes give the same solution – which is also the one provided on p. 214. 5.4.2 Solving using the Jordan form In section 5.3 we Found the eigenvalues oF the matrix A and used these to fnd the matrix V Formed From the set oF linearly independent eigenvectors oF A . The diagonal matrix J = diag( λ 1 ,...,λ n ) (5.6) is the Jordan Form oF A and V is the transition matrix, such that V 1 AV = J (5.7) ±rom this result we have A t = VJ t V 1 and since the solution to the system u t = Au t 1 is u t = A t u 0 , then u t = VJ t V 1 u 0 where J t = λ t 1 0 ··· 0 0 λ t 2 0 . . . . . . . . . 00 λ t n (5.8)
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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.

Ask a homework question - tutors are online