Similarity of Hybrid Numbers

Abstract

The set of hybrid numbers is a noncommutative number system unified and generalized the complex, dual and double(hyperbolic) numbers with the relation ih = −hi = ε + i. Two hybrid numbers p and q are said to be similar if there exist a hybrid number x satisfying the equality x −1 qx = p. And it is denoted by p ∼ q. In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations px = xq and qx − xp = c for p, q, c ∈ K.