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arXiv · 2008.02850

Quaternionic numerical range of complex matrices

Luís Carvalho·Cristina Diogo·Sérgio Mendes
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Abstract

The paper explores further the computation of the quaternionic numerical range of a complex matrix. We prove a modified version of a conjecture by So and Tompson. Specifically, we show that the shape of the quaternionic numerical range for a complex matrix depends on the complex numerical range and two real values. We establish under which conditions the bild of a complex matrix coincides with its complex numerical range and when the quaternionic numerical range is convex.

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Luís Carvalho, Cristina Diogo, Sérgio Mendes. 2020-08-06. Quaternionic numerical range of complex matrices. https://arxiv.org/abs/2008.02850

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