Unified theorems on completions of matrix pencils (Q1180393)

The authors generalize and unify some theorems concerned with the existence of a pencil with a prescribed subpencil and prescribed strict equivalence class. The first theorem unifies a theorem of \textit{R. C. Thompson} [ibid. 24, 1-31 (1979; Zbl 0395.15003)] and two theorems of \textit{I. Zaballa} [ibid. 87, 113-146 (1987; Zbl 0632.15003) and ibid. 101, 9-31 (1988; Zbl 0673.93025)]. The second theorem generalizes the first theorem (when the field is infinite). On the other hand, the second theorem generalizes a theorem of \textit{I. Baragaña} [ibid. 121, 521-535 (1989; Zbl 0678.15012)].