On k-conjugate of Quaternions

Serpil Halıcı, Şule Çürük


In this paper, we investigate some special involutions of the quaternions these are functions of a quaternion variable that are self-inverse. We consider the conjugate of quaternion matrices by the aid of involutions. Moreover, using by the representation matrix we give some matrix identities.

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Chernov, V.M., Discrete Orthogonal Transforms with Data Representation In Composition Algebras, in: Proceedings Scandinavian Conference on Image Analysis, Uppsala, Sweden, 1995, pp. 357–364.

Coxeter H. S. M., Quaternions and reflections. American Mathematical Monthly 53(3) (1946), 136-146.

Ell T. A and Sangwine S. J., Quaternion involutions and anti-involutions. Computers & Mathematics with Appl., Vol. 53, 2007, pp. 137-143.

Erdoğdu, M., and Mustafa Özdemir. On complex split quaternion matrices. Advances in Applied Clifford Algebras 23.3 (2013): 625-638.

Hamilton W. R., Theory of quaternions. Proceedings of the Royal Irish Academy (1836-1869) 3 (1844): 1-16.

Horn, R.A., Johnson, C.R. Matrix Analysis, Cambridge University Press, Cambridge (1990).

Patrick R. Girard, Quaternions, Clifford Algebras and Relativistic Physics, Birkhauser Verlag AG. 2007.

Ward J.P. Quaternions and Cayley Numbers: Algebra and Applications, Mathematics and its Applications, Vol. 403, Kluwer, Dordrecht (1997).

Franklin A. Graybill, Matrices with Applications, In Station Second Edition, 1983, USA.


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Toronto, Ontario, Canada
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