A quaternion q is a 4D number:\[ q = q_{1}\mathbf{i} + q_{2}\mathbf{j} + q_{3}\mathbf{k} + q_{4} \] Or written as a vector: \[ q = [\, q_{1},\, q_{2},\, q_{3},\, q_{4} \,] \] Where: \[ -\ \mathbf{i},\ \mathbf{j},\ \mathbf{k} \text{ are like imaginary unit vectors (just like how complex numbers have } i\text{)} \] \[ -\ q_{1},\ q_{2},\ q_{3} \text{ form a vector part (representing axis)} \] \[ -\..