Mathematical Appendix

Alfonso Novales, Esther Fernández and Jesus Ruiz

Chapter 12 in Economic Growth, 2022, pp 621-645 from Springer

Abstract: Abstract This chapter presents the main mathematical tools used throughout the book: (1) solving the system of equations that characterize the solution to discrete time and continuous time deterministic control problems, with special attention to the transversality conditions that guarantee stable solutions, (2) solving first order difference equations with constant or time varying coefficients, (3) matrix algebra, with particular emphasis in the computation of eigenvalues and eigenvectors, since the Jordan decomposition of the transition matrix of a system of equations plays a central role in the numerical solution of the growth models considered in the book, (4) complex analysis, since the eigenvalues and eigenvectors of the transition matrices that come out of growth models are often complex numbers and vectors.

Keywords: Optimal control problem; Spectral decomposition; Differential equation; Transversality condition; Eigenvalues; Eigenvectors; Complex numbers (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/978-3-662-63982-5_12

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