Emerging Topics in Computer Vision

3.3. Tensor Calculus

Tensor calculus is a natural tool to use when the objects at study are expressed in a specific coordinate system but have physical properties that are independent on the chosen coordinate system. Another advantage is that it gives a simple and compact notation and the rules for tensor algebra make it easy to remember even quite complex formulas. For a more detailed treatment, see [58], and for an engineering approach, see [42].

In this chapter, a simple definition of a tensor and the basic rules for manipulating tensors are given. We start with a straightforward definition:

Definition 19. An affine tensor is an object in a linear space, V, that consists of a collection of numbers that are related to a specific choice of coordinate ...