MATH 545 Applied Linear Algebra#
Instructor#
This is a course given by Andreas Buttenschoen at the University of Massachusetts Amherst.
Description#
Math 545 is an advanced linear algebra course that builds on the concepts and techniques introduced in Math 235 (Intro Linear Algebra). We will study the decomposition of matrices, particularly the LU, QR, Cholesky and SVD decompositions. The coursework will be a mix of proof and computation. We will also study vector spaces and linear transformations, inner product spaces, orthogonality, spectral theory, and Jordan form. We will emphasize applications of these techniques to various problems including solutions of linear systems, least-square fitting, fast Fourier transforms, dynamical systems. The final part covers algorithms for computation of eigenpairs, iterative methods for linear systems, etc.
Learning Goals#
Summarize properties and constructions of matrix decompositions LU, QR, Cholesky and SVD
Perform matrix computations using mathematical software Python, SciPy and Jupyter
Compute solutions of linear systems of equations using matrix decompositions
Compute least squares approximations of linear systems of equations using matrix decompositions
Eigenvalues of matrices.
The Fourier transform.
Iterative methods for linear systems and eigenpairs.
Mathematical Python resources#
Mathematical Python is a great resource to get started with mathematical python.
Course Grading tools#
PLOM Grading will be used to grade quizzes and exams.
License#
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
