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Tensor

Explore Tensor on MathWorld


A tensor is a generalization of scalars, vectors, and matrices to an arbitrary number of indices.

Tensor is a graduate-level concept that would be first encountered in a differential geometry course.

Prerequisites

Scalar: A scalar is value (such as a measurement) that has only magnitude but not direction. This contrasts with a vector, which has direction as well as magnitude.
Tangent Vector: A tangent vector is a vector pointing in the direction of the tangent line to the graph of a function.
Vector: (1) In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. (2) In topology, a vector is an element of a vector space.

Classroom Articles on Differential Geometry (Up to Graduate Level)

  • Curvature
  • Gaussian Curvature
  • Differential Geometry
  • Mean Curvature
  • Differential k-Form
  • Tangent Bundle