The dimension of orbits and bundles of Hermitian pencils under $*$-congruence

Abstract

We provide an explicit formula for the dimension of the $*$-congruence orbits and bundles of Hermitian matrix pencils over the field of complex numbers. The formula is given in terms of the sizes of the canonical blocks in the Hermitian Kronecker canonical form of the pencils. This extends the formulas provided only for the generic orbits and bundles in a previous work.