Logo
Unionpedia
Communication
Get it on Google Play
New! Download Unionpedia on your Android™ device!
Install
Faster access than browser!
 

Conformal group

Index Conformal group

In mathematics, the conformal group of a space is the group of transformations from the space to itself that preserve angles. [1]

49 relations: American Mathematical Monthly, Angle, Biquaternion, Compact space, Complex plane, Conformal geometry, Conformal symmetry, Definite quadratic form, Dual number, Ebenezer Cunningham, Electromagnetic field, Euclidean space, Field (mathematics), Group (mathematics), Harry Bateman, Homography, Homothetic transformation, Hyperbolic angle, Hypersphere, Inversive geometry, Isaak Yaglom, Isotropic quadratic form, Jacobian matrix and determinant, Japan Academy, Kinematics, Lie group, Lie sphere geometry, Light cone, Linear fractional transformation, Lorentz transformation, Ludwik Silberstein, Mathematics, Möbius transformation, Orthogonal group, Orthogonal transformation, Project Euclid, Projective line over a ring, Pseudo-Euclidean space, Quadratic form, Rapidity, Riemann sphere, Ring (mathematics), Special relativity, Sphere, Spherical wave transformation, Split-complex number, Squeeze mapping, University of Chicago Press, University of Liverpool.

American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

New!!: Conformal group and American Mathematical Monthly · See more »

Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

New!!: Conformal group and Angle · See more »

Biquaternion

In abstract algebra, the biquaternions are the numbers, where, and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group.

New!!: Conformal group and Biquaternion · See more »

Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

New!!: Conformal group and Compact space · See more »

Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

New!!: Conformal group and Complex plane · See more »

Conformal geometry

In mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space.

New!!: Conformal group and Conformal geometry · See more »

Conformal symmetry

In mathematical physics, the conformal symmetry of spacetime is expressed by an extension of the Poincaré group.

New!!: Conformal group and Conformal symmetry · See more »

Definite quadratic form

In mathematics, a definite quadratic form is a quadratic form over some real vector space that has the same sign (always positive or always negative) for every nonzero vector of.

New!!: Conformal group and Definite quadratic form · See more »

Dual number

In linear algebra, the dual numbers extend the real numbers by adjoining one new element ε with the property ε2.

New!!: Conformal group and Dual number · See more »

Ebenezer Cunningham

Ebenezer Cunningham (7 May 1881, Hackney, London – 12 February 1977) was a British mathematician who is remembered for his research and exposition at the dawn of special relativity.

New!!: Conformal group and Ebenezer Cunningham · See more »

Electromagnetic field

An electromagnetic field (also EMF or EM field) is a physical field produced by electrically charged objects.

New!!: Conformal group and Electromagnetic field · See more »

Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

New!!: Conformal group and Euclidean space · See more »

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

New!!: Conformal group and Field (mathematics) · See more »

Group (mathematics)

In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.

New!!: Conformal group and Group (mathematics) · See more »

Harry Bateman

Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician.

New!!: Conformal group and Harry Bateman · See more »

Homography

In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive.

New!!: Conformal group and Homography · See more »

Homothetic transformation

In mathematics, a homothety (or homothecy, or homogeneous dilation) is a transformation of an affine space determined by a point S called its center and a nonzero number λ called its ratio, which sends in other words it fixes S, and sends any M to another point N such that the segment SN is on the same line as SM, but scaled by a factor λ. In Euclidean geometry homotheties are the similarities that fix a point and either preserve (if) or reverse (if) the direction of all vectors.

New!!: Conformal group and Homothetic transformation · See more »

Hyperbolic angle

In mathematics, a hyperbolic angle is a geometric figure that divides a hyperbola. The science of hyperbolic angle parallels the relation of an ordinary angle to a circle. The hyperbolic angle is first defined for a "standard position", and subsequently as a measure of an interval on a branch of a hyperbola. A hyperbolic angle in standard position is the angle at (0, 0) between the ray to (1, 1) and the ray to (x, 1/x) where x > 1. The magnitude of the hyperbolic angle is the area of the corresponding hyperbolic sector which is ln x. Note that unlike circular angle, hyperbolic angle is unbounded, as is the function ln x, a fact related to the unbounded nature of the harmonic series. The hyperbolic angle in standard position is considered to be negative when 0 a > 1 so that (a, b) and (c, d) determine an interval on the hyperbola xy.

New!!: Conformal group and Hyperbolic angle · See more »

Hypersphere

In geometry of higher dimensions, a hypersphere is the set of points at a constant distance from a given point called its center.

New!!: Conformal group and Hypersphere · See more »

Inversive geometry

In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion.

New!!: Conformal group and Inversive geometry · See more »

Isaak Yaglom

Isaak Moiseevich Yaglom (Исаа́к Моисе́евич Ягло́м; 6 March 1921 – 17 April 1988) was a Soviet mathematician and author of popular mathematics books, some with his twin Akiva Yaglom.

New!!: Conformal group and Isaak Yaglom · See more »

Isotropic quadratic form

In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero.

New!!: Conformal group and Isotropic quadratic form · See more »

Jacobian matrix and determinant

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.

New!!: Conformal group and Jacobian matrix and determinant · See more »

Japan Academy

is an honorary organization founded in 1879 to bring together leading Japanese scholars with distinguished records of scientific achievements.

New!!: Conformal group and Japan Academy · See more »

Kinematics

Kinematics is a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the mass of each or the forces that caused the motion.

New!!: Conformal group and Kinematics · See more »

Lie group

In mathematics, a Lie group (pronounced "Lee") is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure.

New!!: Conformal group and Lie group · See more »

Lie sphere geometry

Lie sphere geometry is a geometrical theory of planar or spatial geometry in which the fundamental concept is the circle or sphere.

New!!: Conformal group and Lie sphere geometry · See more »

Light cone

In special and general relativity, a light cone is the path that a flash of light, emanating from a single event (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime.

New!!: Conformal group and Light cone · See more »

Linear fractional transformation

In mathematics, the phrase linear fractional transformation usually refers to a Möbius transformation, which is a homography on the complex projective line P(C) where C is the field of complex numbers.

New!!: Conformal group and Linear fractional transformation · See more »

Lorentz transformation

In physics, the Lorentz transformations (or transformation) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.

New!!: Conformal group and Lorentz transformation · See more »

Ludwik Silberstein

Ludwik Silberstein (1872 – 1948) was a Polish-American physicist who helped make special relativity and general relativity staples of university coursework.

New!!: Conformal group and Ludwik Silberstein · See more »

Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Conformal group and Mathematics · See more »

Möbius transformation

In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

New!!: Conformal group and Möbius transformation · See more »

Orthogonal group

In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.

New!!: Conformal group and Orthogonal group · See more »

Orthogonal transformation

In linear algebra, an orthogonal transformation is a linear transformation T: V → V on a real inner product space V, that preserves the inner product.

New!!: Conformal group and Orthogonal transformation · See more »

Project Euclid

Project Euclid is a collaborative partnership between Cornell University Library and Duke University Press which seeks to advance scholarly communication in theoretical and applied mathematics and statistics through partnerships with independent and society publishers.

New!!: Conformal group and Project Euclid · See more »

Projective line over a ring

In mathematics, the projective line over a ring is an extension of the concept of projective line over a field.

New!!: Conformal group and Projective line over a ring · See more »

Pseudo-Euclidean space

In mathematics and theoretical physics, a pseudo-Euclidean space is a finite-dimensional ''n''-space together with a non-degenerate quadratic form.

New!!: Conformal group and Pseudo-Euclidean space · See more »

Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

New!!: Conformal group and Quadratic form · See more »

Rapidity

In relativity, rapidity is commonly used as a measure for relativistic velocity.

New!!: Conformal group and Rapidity · See more »

Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

New!!: Conformal group and Riemann sphere · See more »

Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

New!!: Conformal group and Ring (mathematics) · See more »

Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

New!!: Conformal group and Special relativity · See more »

Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

New!!: Conformal group and Sphere · See more »

Spherical wave transformation

Spherical wave transformations leave the form of spherical waves as well as the laws of optics and electrodynamics invariant in all inertial frames.

New!!: Conformal group and Spherical wave transformation · See more »

Split-complex number

In abstract algebra, a split complex number (or hyperbolic number, also perplex number, double number) has two real number components x and y, and is written z.

New!!: Conformal group and Split-complex number · See more »

Squeeze mapping

In linear algebra, a squeeze mapping is a type of linear map that preserves Euclidean area of regions in the Cartesian plane, but is not a rotation or shear mapping.

New!!: Conformal group and Squeeze mapping · See more »

University of Chicago Press

The University of Chicago Press is the largest and one of the oldest university presses in the United States.

New!!: Conformal group and University of Chicago Press · See more »

University of Liverpool

The University of Liverpool is a public university based in the city of Liverpool, England.

New!!: Conformal group and University of Liverpool · See more »

Redirects here:

Conformal group of space-time, Conformal group of spacetime.

References

[1] https://en.wikipedia.org/wiki/Conformal_group

OutgoingIncoming
Hey! We are on Facebook now! »