Abstract
This chapter discusses tensors and their algebra. Like vectors, tensors are geometric objects having a linear, homogeneous law of transformation. Specifically, scalars and vectors are two kinds of tensors. A scalar is said to be a tensor of rank zero and a vector is said to be a tensor of rank one. The metric tensor is an example of a tensor of rank two. Any tensor of rank two may be represented by the matrix of its components. The latter helps us to visualize the sort of mathematical entity that a tensor is, but it cannot be extended to tensors of higher rank than two. The chapter also discusses tensor calculus and the Riemann–Christoffel tensor.
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