In this paper, we consider split quaternions and split quaternion matrices. Firstly, we give some properties of split quaternions. After that we investigate split quaternion matrices using properties of complex matrices. Then we define the complex adjoint matrix of split quaternion matrices and we describe some of their properties. Furthermore, we give the definition of q-determinant of split quaternion matrices.

The aim of this study is to investigate some properties of complex quaternion and complex split quaternion matrices. To verify this, we use 2x2 complex matrix representation of these quaternions. Moreover, we present a method to find the determinant of complex quaternion and complex split quaternion matrices. Finally, we research some special matrices for quaternions above.

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The purpose of this paper is to determine derivations of the algebra H α,β of generalized quaternions over the reals and hence to obtain the algebra Der(H α,β ) of derivations of H α,β . Once we know derivations we might decompose Der(H α,β ) in terms of its inner and/or central derivations whenever they exist. Apart from Der(H α,β ) we would also be able to obtain generalized derivations, which have been studied by analysts in the context of algebras of some normed spaces, and of prime and semiprime rings.

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