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

Zhuo-Heng He (), Xiao-Na Zhang and Xiaojing Chen
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Zhuo-Heng He: Department of Mathematics, Shanghai University, Shanghai 200444, China
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

Mathematics, 2023, vol. 11, issue 23, 1-14

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.

Keywords: quaternion algebra; covariance matrices; ? -Hermicity; signal processing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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