![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
For a complex -by-
matrix
, the numerical range
is the range of the map
acting on the unit sphere in
. We ask whether the multivalued inverse numerical range map
has a continuous single-valued selection defined on all or part of
. We show that for a large class of matrices,
does have a continuous selection on
. For other matrices,
has a continuous selection defined everywhere on
except in the vicinity of a finite number of exceptional points on the boundary of
.
AMS Subject Classifications:
Acknowledgements
We would like to thank Ilya Spitkovsky for his helpful advice and expertise. Thanks also to Charles Johnson for organizing the summer REU during which this project was started.
Notes
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work was partially supported by NSF [grant number DMS-0751964].