Research seminar in Mathematics, "Canonical forms and their perturbations" by Sweta Das

Abstract

Canonical forms provide a fundamental framework for studying matrices and matrix pencils through invariants under various equivalence transformations. These forms reveal structural information of the underlying objects, e.g., eigenvalues, their multiplicities, and minimal indices. This information plays an important role in differential-algebraic equations, control theory, generalized eigenvalue problems, etc. However, in practical applications, canonical invariants are often sensitive to perturbations arising from measurement errors and numerical computations. This seminar presents an overview of canonical forms and their perturbation theory.