Abstract
In this chapter we build on the basic matrix theory we learned in Chap. 6 and present a number of advanced topics. The techniques and tools we acquire will prove quite useful in many areas of mathematics, economics, computation, and particularly, econometrics. The knowledge of eigenvalues and eigenvectors in Sect. 7.4 are crucial for understanding and solving systems of differential equations in Chap. 17. Such equations, in turn, play an important role in macroeconomic analysis. We shall learn several ways of factoring a matrix into two matrices, techniques which are of immense importance for efficient computation.
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- 1.
The great German mathematician Johann Carl Friedrich Gauss (1777–1855) made contributions to many areas of mathematics including algebra, number theory, geometry, and differential equations.
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Named after the German mathematician Leopold Kronecker (1823–1891), who studied and made contributions to number theory and elliptic functions. He also held views on mathematics contrary to those of his contemporaries such as Cantor and Dedekind.
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© 2011 Springer-Verlag Berlin Heidelberg
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Dadkhah, K. (2011). Advanced Topics in Matrix Algebra. In: Foundations of Mathematical and Computational Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13748-8_7
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DOI: https://doi.org/10.1007/978-3-642-13748-8_7
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