Economics Dynamics Problems 224

Economics Dynamics Problems 224 - 208 Economic Dynamics 5.3...

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208 Economic Dynamics 5.3 Eigenvalues and eigenvectors Let us concentrate on the frst-order linear homogeneous equation system ± x t y t ² = ± ab cd ²± x t 1 y t 1 ² or u t = Au t 1 with solution u t = A t u 0 . We invoke the Following theorem. THEOREM 5.1 If the eigenvalues of the matrix A are r and s obtained from | A λ I |= 0 such that r ±= s, then there exists a matrix V = [ v r v s ] composed of the eigenvectors associated with r and s, respectively, such that D = ± r 0 0 s ² = V 1 AV We shall illustrate this theorem by means oF an example. Example 5.3 Let A = ± 21 12 ² The characteristic equation is
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