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Cramer’s Rules for Some Hermitian Coquaternionic Matrix Equations

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Abstract

In this paper, using row-column determinants previously introduced by the author, properties of the determinant of a Hermitian matrix are investigated, and determinantal representations of the inverse of a Hermitian coquaternionic matrix are given. With their help, Cramer’s rules for left and right systems of linear equations with Hermitian coquaternionic coefficient matrices are obtained. Cramer’s rule for a two-sided coquaternionic matrix equation \(\mathbf{AXB}=\mathbf{D}\) (with Hermitian \(\mathbf{A}\), \(\mathbf{B}\)) is given as well.

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Authors and Affiliations

  1. Pidstrygach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine, str. Naukova 3b, Lviv, 79060, Ukraine

    Ivan Kyrchei

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  1. Ivan Kyrchei
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Correspondence to Ivan Kyrchei.

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Communicated by Rafał Abłamowicz

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Kyrchei, I. Cramer’s Rules for Some Hermitian Coquaternionic Matrix Equations. Adv. Appl. Clifford Algebras 27, 2509–2529 (2017). https://doi.org/10.1007/s00006-016-0751-1

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