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On Complex Split Quaternion Matrices

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Abstract

In this paper, we present some important properties of complex split quaternions and their matrices. We also prove that any complex split quaternion has a 4 × 4 complex matrix representation. On the other hand, we give answers to the following two basic questions “If AB =  I, is it true that BA =  I for complex split quaternion matrices?” and “How can the inverse of a complex split quaternion matrix be found?”. Finally, we give an explicit formula for the inverse of a complex split quaternion matrix by using complex matrices.

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Authors and Affiliations

  1. Department of Mathematics and Computer Sciences, Necmettin Erbakan University, 42060, Konya, Turkey

    Melek Erdoğdu

  2. Department of Mathematics, Akdeniz University, 07058, Antalya, Turkey

    Mustafa Özdemir

Authors
  1. Melek Erdoğdu
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  2. Mustafa Özdemir
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Correspondence to Melek Erdoğdu.

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Erdoğdu, M., Özdemir, M. On Complex Split Quaternion Matrices. Adv. Appl. Clifford Algebras 23, 625–638 (2013). https://doi.org/10.1007/s00006-013-0399-z

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  • DOI: https://doi.org/10.1007/s00006-013-0399-z

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