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Quaternion matrix decomposition and its theoretical implications

Author

Listed:
  • Chang He

    (Shanghai University of Finance and Economics)

  • Bo Jiang

    (Shanghai University of Finance and Economics)

  • Xihua Zhu

    (Shanghai Business School)

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.

Suggested Citation

  • Chang He & Bo Jiang & Xihua Zhu, 2023. "Quaternion matrix decomposition and its theoretical implications," Journal of Global Optimization, Springer, vol. 87(2), pages 741-758, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01210-7
    DOI: 10.1007/s10898-022-01210-7
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    References listed on IDEAS

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    1. Jos F. Sturm & Shuzhong Zhang, 2003. "On Cones of Nonnegative Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 246-267, May.
    2. D. Goldfarb & G. Iyengar, 2003. "Robust Portfolio Selection Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 1-38, February.
    3. Yongwei Huang & Shuzhong Zhang, 2007. "Complex Matrix Decomposition and Quadratic Programming," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 758-768, August.
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