# Numerical ranges and matrix completions

Hadwin, D.W., Harrison, K.J. and Ward, J.A.
(2000)
*Numerical ranges and matrix completions.*
Linear Algebra and its Applications, 315
(1-3).
pp. 145-154.

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## 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.

Item Type: | Journal Article |
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Murdoch Affiliation(s): | School of Mathematical and Physical Sciences |

Publisher: | Elsevier |

Copyright: | 2000 Elsevier Science Inc. |

URI: | http://researchrepository.murdoch.edu.au/id/eprint/17547 |

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