A tensor quantity is a physical quantity that is neither a vector nor a scalar. Tensors are algebraic objects that describe multilinear relationships between sets of algebraic objects related to a vector space. Each point in space in a tensor field has its own tensor, and the magnitude, direction, and plane in which a quantity behaves or is defined in relation to its coordinate system are called tensor quantities.
Some examples of tensor quantities are:
- Stress on a material, such as a bridge building beam
- Volumetric stress and planar stress
- Strain
The order or rank of a tensor is the sum of the orders of its arguments plus the order of the resulting tensor. The order of a tensor determines the type of the tensor, which is a pair of natural numbers (n, m) that determine the precise form of the transformation law. Tensor contraction is an operation that reduces a type (n, m) tensor to a type (n − 1, m − 1) tensor, of which the trace is a special case. It thereby reduces the total order of a tensor by two.
