Rank-one completions of partial matrices and completely rank-nonincreasing linear functionals

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.

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2006-08, Vol.134 (8), p.2169-2178
Main Authors: Hadwin, Don, Harrison, K. J., Ward, J. A.
Format: Article
Language:English
Subjects:
Algebra
Applied mathematics
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Linear transformations
Mathematical theorems
Mathematical vectors
Mathematics
Matrices
Sciences and techniques of general use
Vertices
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Description
Summary: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-06-08094-4