Eigenstructures of low-rank matrix polynomials

Abstract: Challenging and intriguing mathematical problems involving matrix polynomials arise in various applications. These problems often revolve around the eigenstructures of the polynomials, emphasizing the importance of the eigenstructures. In this talk we consider the set of matrix polynomials of bounded rank and degree and describe the eigenstructures that these polynomials typically have, so called generic eigenstructures. We also find such generic eigenstructures for the sets of symmetric and skew-symmetric matrix polynomials. Notably, these symmetries have drastic effect on generic eigenstructures, for example, on whether we can anticipate the appearance of eigenvalues in the eigenstructures or not. This talk is primarily based on joint work with Froilán Dopico and Fernando De Téran.

numerical analysisoptimization and control

Audience: researchers in the discipline

CAM seminar

Series comments: Online streaming via zoom on exceptional cases if requested. Please contact the organizers at the latest Monday 11:45.