Linear algebra is a widely used tool across many scientific disciplines including physics, statistics and pattern matching to name a few, as well as the topic for this book, three-dimensional rotations. The modern relationship between geometry and algebra began with the introduction of Cartesian coordinates by René Descartes in the early seventeenth century. This enabled geometric objects such as lines and planes to be used to solve linear equations. Vector spaces were not discovered until 200 years later and provided a more compact and powerful approach to the purely geometric approach for linear algebra. In addition, vector spaces are used with elements beyond real numbers such as complex numbers and finite fields.