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Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverse

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  • Kyrchei, Ivan

Abstract

Weighted singular value decomposition (WSVD) and a representation of the weighted Moore–Penrose inverse of a quaternion matrix by WSVD have been derived. Using this representation, limit and determinantal representations of the weighted Moore–Penrose inverse of a quaternion matrix have been obtained within the framework of the theory of noncommutative column-row determinants. By using the obtained analogs of the adjoint matrix, we get the Cramer rules for the weighted Moore–Penrose solutions of left and right systems of quaternion linear equations.

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  • Kyrchei, Ivan, 2017. "Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverse," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 1-16.
    • Handle: RePEc:eee:apmaco:v:309:y:2017:i:c:p:1-16
    DOI: 10.1016/j.amc.2017.03.048
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    References listed on IDEAS

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    1. Rehman, Abdur & Wang, Qing-Wen & He, Zhuo-Heng, 2015. "Solution to a system of real quaternion matrix equations encompassing η-Hermicity," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 945-957.
    2. Kyrchei, Ivan, 2015. "Determinantal representations of the W-weighted Drazin inverse over the quaternion skew field," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 453-465.
    3. He, Zhuo-Heng & Wang, Qing-Wen & Zhang, Yang, 2017. "Simultaneous decomposition of quaternion matrices involving η-Hermicity with applications," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 13-35.
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    Cited by:

    1. Xiaoji Liu & Naping Cai, 2018. "High-Order Iterative Methods for the DMP Inverse," Journal of Mathematics, Hindawi, vol. 2018, pages 1-6, May.
    2. Munish Kansal & Manpreet Kaur & Litika Rani & Lorentz Jäntschi, 2023. "A Cubic Class of Iterative Procedures for Finding the Generalized Inverses," Mathematics, MDPI, vol. 11(13), pages 1-18, July.

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