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arXiv · 2311.00849

Winding number criterion for the origin to belong to the numerical range of a matrix on a loop of matrices

Cheng Guo·Shanhui Fan
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Abstract

Let $A:[0,1]\to GL(n,\mathbb{C})$ be continuous with $A(0)=A(1)$, thus the winding number of $\det A$ is well-defined. If the winding number is not divisible by $n$, then the origin belongs to the numerical range of $A(\phi)$ for some $\phi \in [0,1]$.

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Cheng Guo, Shanhui Fan. 2023-11-01. Winding number criterion for the origin to belong to the numerical range of a matrix on a loop of matrices. https://arxiv.org/abs/2311.00849

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