In
mathematics,
physics, and
engineering, a
tensor field assigns a
tensor to each point of a mathematical space (typically a
Euclidean space or
manifold). Tensor fields are used in
differential geometry,
algebraic geometry,
general relativity, in the analysis of
stress and
strain in materials, and in numerous applications in the physical sciences and engineering. As a tensor is a generalization of a
scalar (a pure number representing a value, like length) and a
vector (a geometrical arrow in space), a tensor field is a generalization of a
scalar field or
vector field that assigns, respectively, a scalar or vector to each point of space.