Row or Column Completion of Polynomial Matrices of Given Degree
A. Amparan, Itziar Baragaña, Silvia Marcaida, Alicia Roca · SIAM Journal on Matrix Analysis and Applications · 2024
Abstract. We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column) completion problem of a polynomial matrix of given degree under different prescribed invariants: the whole eigenstructure, all of it but the row (column) minimal indices, and the finite and/or infinite structures. Moreover, we characterize the existence of a polynomial matrix with prescribed degree and eigenstructure over an arbitrary field.