ELA, Volume 3, pp. 103-118, June 1998, abstract.
On the Rodman-Shalom Conjecture Regarding the Jordan Form of
Completions of Partial Upper Triangular Matrices
Cristina Jordan, Juan R. Torregrosa, and Ana M. Urbano
Rodman and Shalom [Linear Algebra and its Applications, 168:221--249,
1992] present a completion problem consisting of characterizing the
existence of a completion of a partial upper triangular matrix A,
with prescribed Jordan form by an inequalities set involving the
minimal rank of the powers of A and the Jordan blocks size of the
completion.
In this paper this problem is solved in two cases: when the minimal
rank of A is 2, and for matrices of size 5 by 5.