July 2004
Intermediate to advanced
688 pages
19h 3m
English
Content preview from Emerging Topics in Computer VisionBecome an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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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 ...
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