Definition:Quaternion/Multiplication

Definition
The product of two quaternions $\mathbf x_1 = a_1 \mathbf 1 + b_1 \mathbf i + c_1 \mathbf j + d_1 \mathbf k$ and $\mathbf x_2 = a_2 \mathbf 1 + b_2 \mathbf i + c_2 \mathbf j + d_2 \mathbf k$ is defined as:

Also see

 * Quaternion Multiplication, where this construction is proved to be consistent with the definition of quaternions.