Scientific journal paper Q1
On the convexity and circularity of the numerical range of nilpotent quaternionic matrices
Luís Carvalho (Carvalho, L.); Sérgio Mendes (Mendes, S.); Cristina Diogo (Diogo, C.);
Journal Title
New York Journal of Mathematics
Year (definitive publication)
2019
Language
English
Country
United States of America
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Times Cited: 6

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Abstract
We provide a sufficient condition for the numerical range of a nilpotent matrix N to be circular in terms of the existence of cycles in an undirected graph associated with N. We prove that if we add to this matrix N a diagonal real matrix D, the matrix D+N has convex numerical range. For 3 x 3 nilpotent matrices, we strength further our results and obtain necessary and sufficient conditions for circularity and convexity of the numerical range.
Acknowledgements
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Keywords
Quaternions,Numerical range,Nilpotent matrix
Fields of Science and Technology Classification
  • Mathematics - Natural Sciences
Funding Records
Funding Reference Funding Entity
PEst-OE/MAT/UI0212/2013 Fundação para a Ciência e a Tecnologia
UID/MAT/04459/2013 Fundação para a Ciência e a Tecnologia
Publication Identifiers
2-s2.0-85077876871
WOS:000505566900001
000505566900001
2-s2.0-85077876871
ci-pub-64430
http://hdl.handle.net/10071/20172
Other Publication Details
2019
Electronic Journals Project
Web of Science©; Scopus;
1076-9803 (print)
1076-9803 (online)
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25
1385 - 1404
Yes
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