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Quaternion matrix decomposition and its theoretical implications

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

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Authors and Affiliations

  1. Research Institute for Interdisciplinary Sciences, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    Chang He

  2. Research Institute for Interdisciplinary Sciences, School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China

    Bo Jiang

  3. Faculty of Business Information, Shanghai Business School, Shanghai, 200235, People’s Republic of China

    Xihua Zhu

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  1. Chang He
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  2. Bo Jiang
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  3. Xihua Zhu
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Correspondence to Bo Jiang.

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Research supported by NSFC Grants 72171141, 72150001 and 11831002, GIFSUFE Grants CXJJ-2019-391, and Program for Innovative Research Team of Shanghai University of Finance and Economics.

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He, C., Jiang, B. & Zhu, X. Quaternion matrix decomposition and its theoretical implications. J Glob Optim 87, 741–758 (2023). https://doi.org/10.1007/s10898-022-01210-7

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