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arXiv · 2106.05072

$m$th roots of $H$-selfadjoint matrices over the quaternions

D. B. Janse van Rensburg·A. C. M. Ran·F. Theron·M. van Straaten
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Abstract

The complex matrix representation for a quaternion matrix is used in this paper to find necessary and sufficient conditions for the existence of an $H$-selfadjoint $m$th root of a given $H$-selfadjoint quaternion matrix. In the process, when such an $H$-selfadjoint $m$th root exists, its construction is also given.

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D. B. Janse van Rensburg, A. C. M. Ran, F. Theron, M. van Straaten. 2021-06-09. $m$th roots of $H$-selfadjoint matrices over the quaternions. https://arxiv.org/abs/2106.05072

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