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Coordinate (other)
Coordinate may refer to: * An element of a coordinate system in geometry and related domains ** Coordinate space in mathematics ** Cartesian coordinate system ** Coordinate (vector space) ** Geographic coordinate system * Coordinate structure in linguistics * Coordinate covalent bond in chemistry * Coordinate descent, an algorithm See also * Coordination (other) Coordination may refer to: * Coordination (linguistics), a compound grammatical construction * Coordination complex, consisting of a central atom or ion and a surrounding array of bound molecules or ions * Coordination number or ligancy of a centr ... * Coordinator (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate System
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the ''x''-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and ''vice versa''; this is the basis of analytic geometry. Common coordinate systems Number line The simplest example of a coordinate system is the identification of points on a line with real numbers using the ''number line''. In this system, an arbitrary point ''O'' (the ''origin'') is chosen on a given line. The coordinate of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Space
In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', may be added together and multiplied ("scaled") by numbers called '' scalars''. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called ''vector axioms''. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space. Vector spaces generalize Euclidean vectors, which allow modeling of physical quantities, such as forces and velocity, that have not only a magnitude, but also a direction. The concept of vector spaces is fundamental for linear algebra, together with the concept of matrix, which allows computing in vector spaces. This provides a concise and synthetic way for manipulating and studying systems of linear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference coordinate line is called a ''coordinate axis'' or just ''axis'' (plural ''axes'') of the system, and the point where they meet is its ''origin'', at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, ''n'' Cartesian coordinates (an element of real ''n''-space) specify the point in an ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate (vector Space)
In mathematics, a set of vectors in a vector space is called a basis if every element of may be written in a unique way as a finite linear combination of elements of . The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to . The elements of a basis are called . Equivalently, a set is a basis if its elements are linearly independent and every element of is a linear combination of elements of . In other words, a basis is a linearly independent spanning set. A vector space can have several bases; however all the bases have the same number of elements, called the ''dimension'' of the vector space. This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces. Definition A basis of a vector space over a field (such as the real numbers or the complex numbers ) is a linearly independent subset of that spans . This mean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geographic Coordinate System
The geographic coordinate system (GCS) is a spherical or ellipsoidal coordinate system for measuring and communicating positions directly on the Earth as latitude and longitude. It is the simplest, oldest and most widely used of the various spatial reference systems that are in use, and forms the basis for most others. Although latitude and longitude form a coordinate tuple like a cartesian coordinate system, the geographic coordinate system is not cartesian because the measurements are angles and are not on a planar surface. A full GCS specification, such as those listed in the EPSG and ISO 19111 standards, also includes a choice of geodetic datum (including an Earth ellipsoid), as different datums will yield different latitude and longitude values for the same location. History The invention of a geographic coordinate system is generally credited to Eratosthenes of Cyrene, who composed his now-lost ''Geography'' at the Library of Alexandria in the 3rd century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Structure
In linguistics, coordination is a complex syntactic structure that links together two or more elements; these elements are called ''conjuncts'' or ''conjoins''. The presence of coordination is often signaled by the appearance of a coordinator (coordinating conjunction), e.g. ''and'', ''or'', ''but'' (in English). The totality of coordinator(s) and conjuncts forming an instance of coordination is called a coordinate structure. The unique properties of coordinate structures have motivated theoretical syntax to draw a broad distinction between coordination and subordination. It is also one of the many constituency tests in linguistics. Coordination is one of the most studied fields in theoretical syntax, but despite decades of intensive examination, theoretical accounts differ significantly and there is no consensus on the best analysis. Coordinators A ''coordinator'' or a coordinating conjunction, often appears between the conjuncts, usually at least between the penultimate and ult ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Covalent Bond
In coordination chemistry, a coordinate covalent bond, also known as a dative bond, dipolar bond, or coordinate bond is a kind of two-center, two-electron covalent bond in which the two electrons derive from the same atom. The bonding of metal ions to ligands involves this kind of interaction. This type of interaction is central to Lewis acid–base theory. Coordinate bonds are commonly found in coordination compounds. Examples Coordinate covalent bonding is ubiquitous. In all metal aquo-complexes (H2O)''n'''m''+, the bonding between water and the metal cation is described as a coordinate covalent bond. Metal-ligand interactions in most organometallic compounds and most coordination compounds are described similarly. The term ''dipolar bond'' is used in organic chemistry for compounds such as amine oxides for which the electronic structure can be described in terms of the basic amine donating two electrons to an oxygen atom. : → O The arrow → indicates that both ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordinate Descent
Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks. A line search along the coordinate direction can be performed at the current iterate to determine the appropriate step size. Coordinate descent is applicable in both differentiable and derivative-free contexts. Description Coordinate descent is based on the idea that the minimization of a multivariable function F(\mathbf) can be achieved by minimizing it along one direction at a time, i.e., solving univariate (or at least much simpler) optimization problems in a loop. In the simplest case of ''cyclic coordinate descent'', one cyclically iterates through the directions, one at a time, minimizing the objec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coordination (other)
Coordination may refer to: * Coordination (linguistics), a compound grammatical construction * Coordination complex, consisting of a central atom or ion and a surrounding array of bound molecules or ions * Coordination number or ligancy of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it * Language coordination, the tendency of people to mimic the language of others * Coordination (political culture), a Utopian form of political regime * Motor coordination, in animal motion * A chemical reaction to form a coordination complex * ''Gleichschaltung'' the process of Nazification in Germany after 1933, often translated as "coordination" See also * Coordinate (other) Coordinate may refer to: * An element of a coordinate system in geometry and related domains ** Coordinate space in mathematics ** Cartesian coordinate system ** Coordinate (vector space) ** Geographic coordinate system * Coordinate structure in li ... * Coordinator (d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
