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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
Einstein notation — In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention useful when dealing with coordinate formulas. It was introduced by Albert Einstein in 1916 … 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
Covariant derivative — In mathematics, the covariant derivative is a way of specifying a derivative along tangent vectors of a manifold. Alternatively, the covariant derivative is a way of introducing and working with a connection on a manifold by means of a… … Wikipedia
Pseudospectral optimal control — Pseudospectral (PS) optimal control is a computational method for solving optimal control problems. PS optimal controllers have beenextensively used to solve a wide range of problems such as those arising in UAV trajectory generation, missile… … Wikipedia
Cotangent space — In differential geometry, one can attach to every point x of a smooth (or differentiable) manifold a vector space called the cotangent space at x. Typically, the cotangent space is defined as the dual space of the tangent space at x, although… … Wikipedia
Outer product — For outer product in geometric algebra, see exterior product. In linear algebra, the outer product typically refers to the tensor product of two vectors. The result of applying the outer product to a pair of vectors is a matrix. The name… … Wikipedia
Intermediate treatment of tensors — In mathematics and physics, a tensor is an idealized geometric or physical quantity whose numerical description, relative to a particular frame of reference, consists of a multiple indexed array of numbers. A vector, for example, is a tensor with … 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
Covariance and contravariance of vectors — For other uses of covariant or contravariant , see covariance and contravariance. In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities… … Wikipedia
