**Metric tensor** — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… … Wikipedia

**Metric tensor (general relativity)** — This article is about metrics in general relativity. For a discussion of metrics in general, see metric tensor. Metric tensor of spacetime in general relativity written as a matrix. In general relativity, the metric tensor (or simply, the metric) … Wikipedia

**Metric** — Metric(s) may refer to: the metric system of measurement International System of Units, or Système International (SI), the modern form of the metric system Metric ton, a measurement of mass equal to 1,000 kg an analytical measurement… … Wikipedia

**Tensor contraction** — In multilinear algebra, a tensor contraction is an operation on one or more tensors that arises from the natural pairing of a finite dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components… … Wikipedia

**Tensor** — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… … Wikipedia

**Metric (mathematics)** — In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric … Wikipedia

**Metric signature** — The signature of a metric tensor (or more generally a nondegenerate symmetric bilinear form, thought of as quadratic form) is the number of positive and negative eigenvalues of the metric. That is, the corresponding real symmetric matrix is… … Wikipedia

**Tensor density** — A tensor density transforms as a tensor, except that it is additionally multiplied or weighted by a power of the Jacobian determinant.For example, a rank 3 tensor density of weight W transforms as::A {ijk}^prime =egin{vmatrix} alpha… … Wikipedia

**Metric compatibility** — This article is about the concept in Riemannian geometry. For the typographic concept, see Typeface#Font metrics. In mathematics, given a metric tensor gab, a covariant derivative is said to be compatible with the metric if the following… … Wikipedia

**Tensor field** — In mathematics, physics and engineering, a tensor field is a very general concept of variable geometric quantity. It is used in differential geometry and the theory of manifolds, in algebraic geometry, in general relativity, in the analysis of… … Wikipedia