#### Conference abstracts

Session B7 - Numerical Linear Algebra

July 15, 16:00 ~ 16:30 - Room B5

## Geometry of matrix polynomial spaces

### Andrii Dmytryshyn

### Umeå University, Sweden - andrii@cs.umu.se

We study how small perturbations of matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy graphs (stratifications) of orbits and bundles of matrix polynomial Fiedler linearizations. We show that the stratification graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler linearizations have the same geometry (topology). We also develop the theory for structure preserving stratification of skew-symmetric matrix polynomials. The results are illustrated by examples using the software tool Stratigraph.

Joint work with Stefan Johansson (Umeå University), Bo Kågström (Umeå University), Paul Van Dooren (Université catholique de Louvain).