208Economic Dynamics5.3 Eigenvalues and eigenvectorsLet us concentrate on the frst-order linear homogeneous equation system±xtyt²=±abcd²±xt−1yt−1²orut=Aut−1with solutionut=Atu0. We invoke the Following theorem.THEOREM 5.1If the eigenvalues of the matrixAare r and s obtained from|A−λI|=0such that r±=s, then there exists a matrixV=[vrvs]composed ofthe eigenvectors associated with r and s, respectively, such thatD=±r00s²=V−1AVWe shall illustrate this theorem by means oF an example.Example 5.3LetA=±2112²The characteristic equation is
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