Harvard AM205 video 5.3 - Gershgorin circle theorem & eigenvalue sensitivity

Harvard Applied Math 205 is a graduate-level course on scientific computing and numerical methods. This video continues Unit 5 of the course on eigenvalue problems. It introduces several useful results for bounding eigenvalues and looking at their sensitivity to matrix perturbations. The Gershgorin circle theorem is derived, which constrains eigenvalues to be within a collection of disks in the complex plane. Then the Bauer–Fike theorem and Weyl's theorem are introduced, to bound how much eigenvalues will move when a matrix is perturbed. For more information see the main course website at https://people.math.wisc.edu/~chr/am205