The Einstein summation convention is used throughout this page. For help with notation, refer to the table of mathematical symbols.
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:
The upper indices [] are the contravariant components, and the lower indices [] are the covariant components.
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:General tensors
A multi-order (general) tensor is simply the tensor product of single order tensors: