Quaternion matrix decomposition and its theoretical implications

Chang He (), Bo Jiang () and Xihua Zhu ()
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Chang He: Shanghai University of Finance and Economics
Bo Jiang: Shanghai University of Finance and Economics
Xihua Zhu: Shanghai Business School

Journal of Global Optimization, 2023, vol. 87, issue 2, No 18, 758 pages

Abstract: Abstract This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in Ai W et al (Math Progr 128(1):253–283, 2011), Huang Y, Zhang S (Math Oper Res 32(3):758–768, 2007), Sturm JF, Zhang S (Math Oper Res 28(2):246–267 2003). The enhanced property can be used to drive some improved results in joint numerical range, $${\mathcal {S}}$$ S -Procedure and quadratically constrained quadratic programming (QCQP) in the quaternion domain, demonstrating the capability of our new decomposition technique.

Keywords: Matrix rank-one decomposition; Quaternion; Joint numerical range; $${\mathcal {S}}$$ S -Procedure; Quadratic optimization; 90C20; 90C30; 90C90; 65F30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01210-7

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