Economics Dynamics Problems 235

Economics Dynamics Problems 235 - Discrete systems of...

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Discrete systems of equations 219 Example 5.7 Next consider the matrix in example 4.11, which is A 3 = ± 34 21 ² then the instructions in each programme are: Mathematica A3={{-3,4},{-2,1}} Eigenvalues[A3] {V3,J3}=JordanDecomposition[A3] MatrixForm /@ {V3,J3} MatrixForm[Inverse[V3].A3.V3] Maple with(linalg): A3:=matrix([[-3,4],[-2,1]]); eigenvals(A3); J3:=jordan(A3,’V3’); print(V3); evalm(V3^(-1)&*A3&*V3); With each programme we get the Jordan form as J 3 = ± 1 + 2 i 0 0 1 2 i ² Verifying the results in theorem 5.3. When considering the stability of the system u t = Au t 1 (5.9) we can approach this from a slightly different perspective, which can provide some valuable insight into the phase portrait of discrete systems. What we intend to do
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