In this lecture we continued our exploration of multiplying two quaternions.

We found that we could reduce our previous polynomial expansion into an easy to read formula and in the process, discovered how both the dot and cross product of two vectors were originally used to help with quaternion multiplication.

We then looked at how to construct a 4x4 matrix for quaternion multiplication.

As a challenge, you were asked to try multiplying the quaternions:

(1 + 2i + 3j + 4k) (5 + 6i + 7j + 8k)

Of the three multiplication options we looked at; which did you use, and which is your favourite?