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Two-sided linear split quaternionic equations with n unknowns. (English) Zbl 1311.15005
The split quaternions, a similar concept to Hamilton quaternions, are generalizations of complex numbers to higher dimension. The algebra of the split quaternions is a $$4$$-dimensional real algebra containing zero divisors, nilpotent elements and nontrivial idempotents. In this paper, the authors consider the linear split quaternionic equations with terms of the form $$axb$$. They present a method of solving such equations with several unknowns, with examples as illustrations.

##### MSC:
 15A06 Linear equations (linear algebraic aspects) 15B33 Matrices over special rings (quaternions, finite fields, etc.) 11R52 Quaternion and other division algebras: arithmetic, zeta functions
##### Keywords:
quaternions; split quaternions; linear quaternion equations
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##### References:
 [1] DOI: 10.1007/978-1-4612-3650-4 · doi:10.1007/978-1-4612-3650-4 [2] Cockle J, Phil. Mag 35 pp 434– (1849) [3] DOI: 10.4134/JKMS.2007.44.6.1313 · Zbl 1140.15016 · doi:10.4134/JKMS.2007.44.6.1313 [4] DOI: 10.1016/j.geomphys.2005.02.004 · Zbl 1088.53010 · doi:10.1016/j.geomphys.2005.02.004 [5] DOI: 10.1016/j.aml.2008.03.020 · Zbl 1163.15303 · doi:10.1016/j.aml.2008.03.020 [6] Özdemir M, Conf. Jangjeon Math. Soc 16 pp 108– (2005) [7] Brody DC, J. Phys. A: Math. Theory 44 pp 1– (2011) [8] DOI: 10.1007/s00006-010-0264-2 · Zbl 1226.15002 · doi:10.1007/s00006-010-0264-2 [9] DOI: 10.1007/s00211-009-0274-y · Zbl 1190.65075 · doi:10.1007/s00211-009-0274-y [10] Alagöz Y, Miskolc Math. Notes 13 pp 223– (2012)
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