Quaternion matrix decomposition and its theoretical implications

2021/09/12 by Chang He, Bo Jiang, He, Chang +3
Computer Science · Mathematics · Engineering · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Inertial Sensor and Navigation

paper · pdf · doi:10.48550/arxiv.2109.05405

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, S-Procedure and quadratically constrained quadratic programming (QCQP) in the quaternion domain, demonstrating the capability of our new decomposition technique.

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