Overview of Quaternions

A detailed tutorial on quaternions. Step by step tutorial including several examples and a visual example of what a quaternion is for reference.

Quaternions form a four-dimensional normed division algebra over real numbers. The original quaternions that were described in mathematics had a slightly definition – they formed a noncommutative number system that extends the complex numbers. However, the most recent definition, the one that is used in mathematics today, is the first one that was given. Quaternions are often denoted as the letter H, often written in the same script style as the number sets R and N. H in this case stands for Hamilton, named after the mathematician who first introduced quaternions to math.