quaternion multiplication

Quaternion Multiplication Formula

Quaternion Multiplication Formula

\begin{align*} (a_1+b_1i+c_1j+d_1k)\odot (a_2+b_2i+c_2j+d_2k) &= (a_1a_2 - b_1b_2 - c_1c_2 - d_1d_2)\\ &\quad + (a_1b_2 + b_1a_2 + c_1d_2 - d_1c_2)i\\ &\quad + (a_1c_2 + c_1a_2 + d_1b_2 - b_1d_2)j \\ &\quad+ (a_1d_2 + d_1a_2 + b_1c_2 - c_1b_2)k. \end{align*}

Enter values for quaternion components to display the quaternion multiplication formula:

Quaternion 1 (a1, b1, c1, d1):
a1:
b1:
c1:
d1:

Quaternion 2 (a2, b2, c2, d2):
a2:
b2:
c2:
d2:

Quaternion Multiplication Formula: