February 2006
Intermediate to advanced
600 pages
8h 57m
English
In this chapter we continue to lay the foundation for quaternion visualization methods, examining first the geometric interpretation of the algebra of complex numbers and then extending that intuition into the quaternion domain. As we will see, the quaternion algebra itself has a geometric interpretation that includes complex numbers as a subalgebra, and the results of algebraic operations can be visualized using geometric methods.
In our context, an algebra is a rule for the combination of sets of numbers. We encounter one particular algebra frequently in ordinary scientific computation: the algebra of complex numbers. The quaternion algebra is one of only two possible generalizations ...