关于四元数数值域截面凸性的注记
A note on convexity of sections of quaternionic numerical range
摘要：
四元数环上矩阵的四元数数值域不一定是凸的。证明了Toeplitz-Hausdorff定理，即对任意给定的四元数矩阵，其四元数数值域的每一部分都是凸的。本文给出了四元数上矩阵的四元数数值域为凸的几个等价条件，并证明了几个数值半径不等式。
英文摘要：
The quaternionic numerical range of matrices over the ring of quaternions is not necessarily convex. We prove Toeplitz-Hausdorff like theorem, that is, for any given quaternionic matrix every section of its quaternionic numerical range is convex. We provide some additional equivalent conditions for the quaternionic numerical range of matrices over quaternions to be convex and prove some numerical radius inequalities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
