Economics Dynamics Problems 234

Economics Dynamics Problems 234 - 218 Economic Dynamics of...

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218 Economic Dynamics of n equations, this requires knowledge of Jordan blocks. Here we shall simply state a result for a 2 × 2 system. THEOREM 5.3 If A is a 2 × 2 matrix, then there is a transition matrix V such that (a) V 1 AV = J 1 = ± r 0 0 s ² for real distinct roots r and s (b) V 1 = J 2 = ± λ 1 0 λ ² for repeated root λ (c) V 1 = J 3 = ± α + β i 0 0 α β i ² for complex conjugate roots λ = α ± β i In each case, J i is the Jordan form of the particular matrix A . We shall use theorem 5.3 when discussing the stability of discrete systems in section 5.6. Section 5.2 dealt with case (a) in detail. Here we shall consider just one example of cases (b) and (c), using both
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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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