ELA, Volume 2, pp. 9-16, July 1997, abstract.

Spectrum preserving lower triangular completions---the nonnegative 
nilpotent case

Abraham Berman and Mark Krupnik

Nonnegative nilpotent lower triangular completions of a nonnegative
nilpotent matrix are studied. It is shown that for every natural number
between the index of the matrix and its order, there exists a completion
that has this number as its index. A similar result is obtained for the
rank. However, unlike the case of complex completions of complex matrices, 
it is proved that for every nonincreasing sequence of nonnegative integers 
whose sum is n, there exists an n by n$ nonnegative nilpotent matrix A 
such that for every nonnegative nilpotent lower triangular completion, B, 
of A, B not equal to A, ind(B) > ind(A).