Rank-one completions of partial matrices and completely rank-nonincreasing linear functionals
Don Hadwin, Kenneth J. Harrison, J.A. Ward · Proceedings of the American Mathematical Society · 2006
We obtain necessary and sufficient conditions for the existence and the uniqueness of rank-one completions of a partial matrix, and we verify a conjecture of Hadwin and Larson concerning the nature of completely rank-nonincreasing linear functionals defined on pattern subspaces.