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Unitary Diagonalization of the Generalized Complementary Covariance Quaternion Matrices with Application in Signal Processing

Author

Listed:
  • Zhuo-Heng He

    (Department of Mathematics, Shanghai University, Shanghai 200444, China
    These authors contributed equally to this work.)

  • Xiao-Na Zhang

    (Department of Mathematics, Shanghai University, Shanghai 200444, China)

  • Xiaojing Chen

    (School of Finance, Shanghai University of International Business and Economics, Shanghai 201620, China
    These authors contributed equally to this work.)

Abstract

Let H denote the quaternion algebra. This paper investigates the generalized complementary covariance, which is the ϕ -Hermitian quaternion matrix. We give the properties of the generalized complementary covariance matrices. In addition, we explore the unitary diagonalization of the covariance and generalized complementary covariance. Moreover, we give the generalized quaternion unitary transform algorithm and test the performance by numerical simulation.

Suggested Citation

  • Zhuo-Heng He & Xiao-Na Zhang & Xiaojing Chen, 2023. "Unitary Diagonalization of the Generalized Complementary Covariance Quaternion Matrices with Application in Signal Processing," Mathematics, MDPI, vol. 11(23), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4840-:d:1292515
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    References listed on IDEAS

    as
    1. Jian-wu Tao & Wen-xiu Chang, 2014. "Adaptive Beamforming Based on Complex Quaternion Processes," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, June.
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