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.