eigenvectorveld
An eigenvectorveld, or eigenvector field, is a vector field that assigns to each point x in a domain a nonzero eigenvector of a matrix-valued function A(x). In other words, for each x, there exists an eigenvalue λ(x) with A(x) v(x) = λ(x) v(x), where v(x) is the eigenvector associated with that eigenvalue. The domain is typically a subset of Euclidean space or a smooth manifold, and A is assumed to vary with x, often smoothly.
Existence and smoothness of an eigenvectorveld depend on the spectral properties of A. If A(x) depends smoothly
Global existence can be hindered by topology. Even when local smooth eigenvectorfields exist, a global, nonvanishing
Applications and examples: in physics and engineering, A(x) often represents a tensor field (such as a diffusion,
See also: eigenvalues, eigenvectors, tensor fields, spectral theory, principal directions.