tangent basis
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tangent line — In geometry, a line that intersects a circle exactly once; in calculus, a line that touches a curve at one point and whose slope is equal to that of the curve at that point. Particularly useful as approximations of curves in the immediate… … Universalium
The Tangent — Infobox Musical artist Name = The Tangent Img capt = Img size = Landscape = Background = group or band Birth name = Alias = Born = Died = Origin = Instrument = Voice type = Genre = Progressive rock Occupation = Years active = 2002–present Label … Wikipedia
Coordinate-induced basis — In mathematics, a coordinate induced basis is a basis for the tangent space or cotangent space of a manifold that is induced by a certain coordinate system. Given the coordinate system xa, the coordinate induced basis ea of the tangent space is… … Wikipedia
Darboux basis — A Darboux basis may refer either to: A Darboux basis of a symplectic vector space In differential geometry, a Darboux frame on a surface. A Darboux tangent in the dovetail joint. This disambiguation page lists articles associated with the same… … Wikipedia
Covariant transformation — See also Covariance and contravariance of vectors In physics, a covariant transformation is a rule (specified below), that describes how certain physical entities change under a change of coordinate system. In particular the term is used for… … Wikipedia
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
Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… … Wikipedia
mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… … Universalium
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
Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… … Wikipedia
Affine connection — An affine connection on the sphere rolls the affine tangent plane from one point to another. As it does so, the point of contact traces out a curve in the plane: the development. In the branch of mathematics called differential geometry, an… … Wikipedia
