Exploring quaternion spaces

As we saw in Chapter 13, Understanding the Importance of Matrices, 4 x 4 matrices are important in graphics as they allow for easy multiplication of compound transformations. Although I didn’t make a big deal of it at the time, these matrices are, in fact, four-dimensional as they have four columns and four rows. Just as we need 4 x 4 matrices to multiply transformation operations, Hamilton found he could use them to find quotients of 3D values. However, the process is a little more complex than how we just created a w dimension for coordinates with a 1 or a 0 on the end for (x, y, z, w).

So, where did Hamilton find his fourth dimension? He had to add another number system and he turned to complex numbers. If you aren’t familiar with complex numbers, then take a look at the explanation here: https://en.wikipedia.org/wiki/Complex_number.

In short, complex numbers were devised for solving quadratic equations and to come up with a solution...