Journal article
Numerical ranges and matrix completions
Linear Algebra and its Applications, Vol.315(1-3), pp.145-154
2000
Abstract
There are two natural ways of defining the numerical range of a partial matrix. We show that for each partial matrix supported on a given pattern they give the same convex subset of the complex plane if and only if a graph associated with the pattern is chordal. This extends a previously known result (C.R. Johnson, M.E. Lundquist, Operator Theory: Adv. Appl. 50 (1991) 283–291) to patterns that are not necessarily reflexive and symmetric, and our proof overcomes an apparent gap in the proof given in the above-mentioned reference. We also define a stronger completion property that we show is equivalent to the pattern being an equivalence.
Details
- Title
- Numerical ranges and matrix completions
- Authors/Creators
- D.W. Hadwin (Author/Creator) - University of New HampshireK.J. Harrison (Author/Creator) - Murdoch UniversityJ.A. Ward (Author/Creator) - Murdoch University
- Publication Details
- Linear Algebra and its Applications, Vol.315(1-3), pp.145-154
- Publisher
- Elsevier
- Identifiers
- 991005541216207891
- Copyright
- 2000 Elsevier Science Inc.
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
- Domestic collaboration
- International collaboration
- Citation topics
- 9 Mathematics
- 9.50 Applied Statistics & Probability
- 9.50.1025 Operator Theory
- Web Of Science research areas
- Mathematics
- Mathematics, Applied
- ESI research areas
- Mathematics