Quaternion matrix decomposition and its theoretical implications

Abstract

This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in [1,21,35]. 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.