The c-numerical range of a quaternion skew-Hermitian matrix is convex

IF 0.8 Q2 MATHEMATICS Advances in Operator Theory Pub Date : 2024-10-14 DOI:10.1007/s43036-024-00391-0
Alma van der Merwe, Madelein Thiersen, Hugo J. Woerdeman
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Abstract

We show that the c-numerical range of a non-scalar skew-Hermitian quaternion matrix is convex. In fact, included in our result is that the c-numerical range of a skew-Hermitian matrix is a rotation invariant subset of the quaternions with zero real parts.

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四元偏斜-赫米特矩阵的 c 数值范围是凸的
我们证明了非标度偏斜-赫米特四元数矩阵的 c 数值范围是凸的。事实上,我们的结果还包括:偏斜-赫米特矩阵的 c 数值范围是实部为零的四元数的旋转不变子集。
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CiteScore
1.60
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0.00%
发文量
55
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