Advanced Linear Algebra

3 Credits · Level: Graduate, Undergraduate

This is a PhD-level course that covers the rigorous treatment of vector and inner product spaces, LU factorization, QR factorization, spectral theorem and singular value decomposition, Jordan form, positive definite matrices, quadratic forms, partitioned matrices, and norms and numerical issues. Further topics may include the Cayley-Hamilton Theorem, the Cauchy-Binet Formula, the Dunford decomposition, and the Theorem by Toeplitz-Hausdorff. This class provides preparation for the linear algebra portion of the Comprehensive Exam.