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AIMS Mathematics

2020, Volume 5, Issue 3: 2211-2225. doi: 10.3934/math.2020146
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Research article

A general method for solving linear matrix equations of elliptic biquaternions with applications

  • Department of Mathematics, Sakarya University, Sakarya, TR-54187, Turkey
  • Received: 05 November 2019 Accepted: 21 February 2020 Published: 28 February 2020

  • MSC : 11R52, 15B33, 15A24

  • In this study, we obtain the real representations of elliptic biquaternion matrices. Afterwards, with the aid of these representations, we develop a general method to solve the linear matrix equations over the elliptic biquaternion algebra. Also we apply this method to the well known matrix equations X - AXB = C and AX - XB = C over the elliptic biquaternion algebra. Then, we give some illustrative numerical examples to show how the aforementioned method and its results work. Furthermore, we provide numerical algorithms for all the problems considered in this paper. Elliptic biquaternions are generalized form of complex quaternions and so real quaternions. This relation is valid for their matrices, as well. Thus, the obtained results extend, generalize and complement some known results from the literature.

    Citation: Kahraman Esen Özen. A general method for solving linear matrix equations of elliptic biquaternions with applications[J]. AIMS Mathematics, 2020, 5(3): 2211-2225. doi: 10.3934/math.2020146

    Related Papers:

  • In this study, we obtain the real representations of elliptic biquaternion matrices. Afterwards, with the aid of these representations, we develop a general method to solve the linear matrix equations over the elliptic biquaternion algebra. Also we apply this method to the well known matrix equations X - AXB = C and AX - XB = C over the elliptic biquaternion algebra. Then, we give some illustrative numerical examples to show how the aforementioned method and its results work. Furthermore, we provide numerical algorithms for all the problems considered in this paper. Elliptic biquaternions are generalized form of complex quaternions and so real quaternions. This relation is valid for their matrices, as well. Thus, the obtained results extend, generalize and complement some known results from the literature.


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