Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations

[EN] We solve the problem of determining the Weierstrass structure of a regular matrix pencil obtained by a low rank perturbation of another regular matrix pencil. We apply the result to find necessary and sufficient conditions for the existence of a low rank perturbation such that the perturbed pencil has prescribed eigenvalues and algebraic multiplicities. The results hold over fields with sufficient number of elements.The work of the first and second authors was partially supported by MINECO grants MTM2017-83624-P and MTM2017-90682-REDT. The work of the first author was also partially supported by UPV/EHU grant GIU16/42.Baragana Garate, I.; Roca Martinez, A. (2019). Weierstrass Structure and Eigenvalue Placement of Regular Matrix Pencils under Low Rank Perturbations. SIAM Journal on Matrix Analysis and Applications. 40(2):440-453. https://doi.org/10.1137/18M1200245S44045340