Topics in Linear Algebra and Convexity
Topic varies by year. 2022-23: Matrix Analysis. This class develops some foundational results about matrices that have wide application in computational mathematics, statistics, engineering, and related fields. Tools from analysis (real, complex, functional, convex) play a key role. Topics may include multilinear algebra, majorization and doubly stochastic matrices, variational principles for eigenvalues, eigenvalue localization regions, unitarily invariant norms, operator monotonicity and convexity, convexity of matrix functions, matrix means, matrix inequalities, perturbation theory, tensor products and linear matrix equations, Hadamard products, nonnegative matrices, positive and completely positive linear maps, positive-definite functions. Not offered 2022-23.
The online version of the Caltech Catalog is provided as a convenience; however, the printed version is the only authoritative source of information about course offerings, option requirements, graduation requirements, and other important topics.