Quaternion matrix decomposition and its theoretical implications

Chang He; Bo Jiang; Xihua Zhu

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arXiv · 2109.05405

Quaternion matrix decomposition and its theoretical implications

Chang He·Bo Jiang·Xihua Zhu

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Abstract

This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to drive some improved results in joint numerical range, $\mathcal{S}$-Procedure and quadratically constrained quadratic programming (QCQP) in the quaternion domain, demonstrating the capability of our new decomposition technique.

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Chang He, Bo Jiang, Xihua Zhu. 2021-09-12. Quaternion matrix decomposition and its theoretical implications. https://arxiv.org/abs/2109.05405

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