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 x^a, the coordinate-induced basis e_a of the tangent space is given by

$e_a = \frac{\partial}{\partial x^a}$

and the dual basis ω^a of the cotangent space is

$\omega^a=dx^a. \,$

References

• D.J. Hurley, M.A. Vandyck Topics in Differential Geometry: a New Approach Using D-Differentiation (2002 Springer) p. 5

This geometry-related article is a stub. You can help Wikipedia by expanding it.v · Categories: Differential geometry Geometry stubs Wikimedia Foundation. 2010. Игры ⚽ Нужна курсовая? Amber (song) Erzya writers Look at other dictionaries: List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   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 china — /chuy neuh/, n. 1. a translucent ceramic material, biscuit fired at a high temperature, its glaze fired at a low temperature. 2. any porcelain ware. 3. plates, cups, saucers, etc., collectively. 4. figurines made of porcelain or ceramic material …   Universalium China — /chuy neuh/, n. 1. People s Republic of, a country in E Asia. 1,221,591,778; 3,691,502 sq. mi. (9,560,990 sq. km). Cap.: Beijing. 2. Republic of. Also called Nationalist China. a republic consisting mainly of the island of Taiwan off the SE coast …   Universalium international relations — a branch of political science dealing with the relations between nations. [1970 75] * * * Study of the relations of states with each other and with international organizations and certain subnational entities (e.g., bureaucracies and political… …   Universalium HISTORICAL SURVEY: THE STATE AND ITS ANTECEDENTS (1880–2006) — Introduction It took the new Jewish nation about 70 years to emerge as the State of Israel. The immediate stimulus that initiated the modern return to Zion was the disappointment, in the last quarter of the 19th century, of the expectation that… …   Encyclopedia of Judaism 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 education — /ej oo kay sheuhn/, n. 1. the act or process of imparting or acquiring general knowledge, developing the powers of reasoning and judgment, and generally of preparing oneself or others intellectually for mature life. 2. the act or process of… …   Universalium chemical bonding — ▪ chemistry Introduction       any of the interactions that account for the association of atoms into molecules, ions, crystals, and other stable species that make up the familiar substances of the everyday world. When atoms approach one another …   Universalium environment — environmental, adj. environmentally, adv. /en vuy reuhn meuhnt, vuy euhrn /, n. 1. the aggregate of surrounding things, conditions, or influences; surroundings; milieu. 2. Ecol. the air, water, minerals, organisms, and all other external factors… …   Universalium 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”