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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Don Hadwin, K. J. Harrison and J. A. Ward
Journal: Proc. Amer. Math. Soc. 134 (2006), 2169-2178
MSC (2000): Primary 15A60
Published electronically: March 20, 2006
MathSciNet review: 2213688
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Abstract: 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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Additional Information

Don Hadwin
Affiliation: Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824
Email: don@cisunix.unh.edu

K. J. Harrison
Affiliation: School of Mathematical and Physical Sciences, Murdoch University, Murdoch, W.A. 6150, Australia
Email: K.Harrison@murdoch.edu.au

J. A. Ward
Affiliation: Faculty of Science, Curtin University, Bentley, W.A. 6102, Australia
Email: J.Ward@exchange.curtin.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08094-4
PII: S 0002-9939(06)08094-4
Received by editor(s): April 23, 2002
Received by editor(s) in revised form: July 15, 2004
Published electronically: March 20, 2006
Communicated by: David R. Larson
Article copyright: © Copyright 2006 American Mathematical Society