Applied Matrix Theory

Catalog description

The purpose of this course is to present fundamental mathematical concepts in matrix theory, essential for contemporary approaches in data analysis, scientific computing, optimization, and virtually all quantitative domains in science and engineering. Topics covered include fundamental matrix operations, SVD, matrix factorizations, Jordan canonical form theorem, Hermitian matrices, algebraic and analytic properties of norms, duality and geometric properties of norms, vector norms, and condition numbers for inverse and linear system. Although the selection of topics is influenced by their application in diverse fields, the course will prioritize exploring the theoretical and conceptual foundations of this subject, aligning with the approach taken in other applied mathematics courses.