Classical treatment of tensorsThe following is a component-based "classical" treatment of tensors. See Component-free treatment of tensors for a modern abstract treatment, and Intermediate treatment of tensors for an approach which bridges the two.
A tensor is a generalization of the concept of vector and matrices. Tensors allow one to express physical laws in a form that applies to any coordinate system. For this reason, they are used extensively in continuum mechanics and the theory of relativity.
A tensor is an invariant multi-dimensional transformation, that takes forms in one coordinate system into another. It takes the form:
|Table of contents|
2 General tensors
3 More about tensors
4 Further Reading
Contravariant and covariant tensors
A contravariant tensor of order 1() is defined as:
A covariant tensor of order 1() is defined as:
A multi-order (general) tensor is simply the tensor product of single order tensors: