Português
A bridge between quaternionic and complex numerical ranges
Event Title
New Trends in Quaternions and Octonions
Year (definitive publication)
2020
Language
English
Country
Portugal
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Abstract
We obtain a sufficient condition for the convexity of quaternionic numerical range for complex matrices in terms of its complex numerical range. It is also shown that the Bild coincides with complex numerical range for real matrices. From this result we derive that all real matrices have convex quaternionic numerical range. As an example we fully characterize the quaternionic numerical range of 2×2 real matrices.
Acknowledgements
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Keywords
Quaternions,Complex numerical range,Quaternionic numerical range
