Some Advanced Topics in Linear Algebra

In this chapter we consider diree important advanced topics in matrix algebra: vector spaces, eigenvalues, and quadratic forms. All play important roles in a variety of contexts in economic theory and in econometrics. Vector spaces enable us to talk about distance between points, and linear dependence between vectors. They are therefore closely linked to die study of systems of linear equations of chapter 7. Eigenvalues play an important role in determining the stability properties of dynamic. linear systems and so this topic is of use in chapters 18,20, 21. 23. and 24. Quadratic forms have applications in econometrics, some of which are illustrated in this chapter, and to the study of second-order derivatives in multivariate calculus discussed in chapter 11.

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