High school teachers teaching vector operations refer to the three unit vectors i, j, and k, but probably don't realize where they come from. [br][br]Quaternions are a number system that extends the complex numbers by introducing three quaternion units i, j, and k. A quaternion is the sum of a real number and real multiples of these quaternion units, [i]q[/i] = [i]w[/i] + [i]xi[/i] + [i]yj[/i] + [i]zk[/i].[br][br]Quaternion multiplication is non-commutative.