ABSTRACT
The orientation of a coordinate system is preserved by rotations. This chapter compares the coordinates of a given point in different coordinate systems. It deals with linear mappings of a 2-dimensional space. It is possible to express every linear mapping as a product of shears and a dilation. The triple product can be used to give an invariant definition of the vector product. The chapter considers some examples of orthogonal transformations in two and three dimensions. It also considers the matrix of transformation when a right-handed rectangular system is rotated about the 3-axis. The chapter shows that every proper orthogonal transformation represents a rotation.
