On Characteristic Invariants of Matrix Pencils and Linear Relations
Hannes Gernandt, Francisco Martínez Pería, Friedrich Philipp, Carsten Trunk · SIAM Journal on Matrix Analysis and Applications · 2023
Abstract. The relationship between linear relations and matrix pencils is investigated. Given a linear relation, we introduce its Weyr characteristic. If the linear relation is the range (or the kernel) representation of a given matrix pencil, we show that there is a correspondence between this characteristic and the Kronecker canonical form of the pencil. This relationship is exploited to obtain estimations on the invariant characteristics of matrix pencils under rank-one perturbations.