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

Keywords : Hybrid numbers, quaternions, coquaternions, dual and double numbers.

MSC Classification : 15A66, 11R52, 15A18, 15A06, 16S50.