Comments on differentiable over function of split quaternions

Abstract

The theory of mathematical analysis over split quaternions is formulated in a closest possible analogy to the usual theory of analytic functions of a complex variable. After reviewing split quaternion algebra via an isomorphic 4 £ 4 matrix representation, a different definition is given to partial derivatives involving split quaternions. This takes care of the ambiguity involved in the no commutative properties of split quaternions. A closely analogous condition for analyticity of functions of a split quaternion variable is found. The analogy with complex variables is illustrated for both the derivative.