On the jordan form of completions of partial upper triangular matrices Original Research Article

Rodman and Shalom present in Linear Algebra Appl. 168:221–249 (1992) two completion conjectures for partial upper triangular matrices. In this paper we show that one of them is not true in general, and we prove its validity for some particular cases. We also prove the equivalence between the two conjectures in the case of partial Hessenberg matrices.