MATH 5524 is a graduate survey of applicable topics in matrix analysis.Students are expected to arrive with a foundation in basic linear algebraat the undergraduate level.Topics will include: spectral theory, variational properties of eigenvalues, singluar values, eigenvalue perturbation theory, functions of matrices and dynamical systems, nonnegative matrices and Perron-Frobenius theory.
You might enjoy dipping in to a few of these supplmental titlesRajendra Bhatia, Matrix Analysis, Springer, 1997.Virginia Tech students have online access to this text.This book gives particularly strong coverage to eigenvalue majorization and classical eigenvalue perturbation theory. Harry Dym, Linear Algebra in Action, 2nd ed., AMS, 2013.Available via Virginia Tech library (2 hour reserve): QA184 .D96 2014 This book makes particularly good use of complex analysis as a fundamental tool for matrix analysis.Roger A. Horn and Charles R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991.Virginia Tech students have online access to this text.This companion to their Matrix Analyis text provides a detailed treatment of the field of values, Sylvester and Lyapunov equations, and functions of matrices, among other topics.Peter Lancaster and Miron Tismenetsky, Theory of Matrices, with Applications, 2nd ed., Academic Press, 1985.Classic text on advanced matrix theory, particularly strong on canonical forms and matrix polynomials.Peter Lax, Linear Algebra and Its Applications, Wiley, 2007.Strong on matrix calculus, avoidance of eigenvalue crossings, abstract normed vector spaces.
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