This is a list of some of the most commonly used coordinate transformations. Let ( x , y ) {\displaystyle (x,y)} be the standard Cartesian coordinates...

composed of a number of different types of conversion: format change of geographic coordinates, conversion of coordinate systems, or transformation to different...

Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely by a pair of real...

frequencies. Mathematics portal Curvilinear coordinates List of common coordinate transformations Log-polar coordinates Polar decomposition Unit circle...

are nn transformations and (n+1)n partial transformations. Coordinate transformation Data transformation (statistics) Geometric transformation Infinitesimal...

an axis of rotation. Each coordinate system is named after its choice of fundamental plane. The following table lists the common coordinate systems in...

hyperplane at infinity of a projective space, the affine transformations are the projective transformations of that projective space that leave the hyperplane...

In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates...

of coordinate systems have been specified for use around the world or in specific regions and for various purposes, necessitating transformations between...

A geographic coordinate system (GCS) is a spherical or geodetic coordinate system for measuring and communicating positions directly on Earth as latitude...

{\varphi }}}+{\ddot {z}}\,{\hat {\boldsymbol {z}}}} List of canonical coordinate transformations Vector fields in cylindrical and spherical coordinates...

also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation...

analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic...

a public registry of geodetic datums, spatial reference systems, Earth ellipsoids, coordinate transformations and related units of measurement, originated...

_{a}^{b}{\sqrt {(dx)^{2}+(dy)^{2}}}\,.} The Euclidean metric in some other common coordinate systems can be written as follows. Polar coordinates (r, θ): x = r...

orthogonal transformations. Area is invariant under linear maps which have determinant ±1 (see Equiareal map § Linear transformations). Some invariants of projective...

the real coordinate space or real coordinate n-space, of dimension n, denoted Rn or R n {\displaystyle \mathbb {R} ^{n}} , is the set of all ordered...

(Bogoliubov) transformations of a quantum state of light. In turn, the Bloch-Messiah decomposition (2) means that such an arbitrary Gaussian transformation can...

symplectic geometry and canonical transformations are generalized by contact transformations, so the 19th century definition of canonical coordinates in classical...

example of a contravariant tensor, has components that transform inversely to the transformation of the reference axes, (with example transformations including...

group (of a particular space). But in mechanics and, more generally, in physics, this concept is frequently understood as a coordinate transformation (importantly...

linear transformation, and a special case of homothetic transformation (scaling about a point). In most cases, the homothetic transformations are non-linear...

between events. Calling one set of transformations the normal Lorentz transformations and the other the inverse transformations is misleading, since there...

called a regular coordinate transformation or regular variable substitution, where regular refers to the C r {\displaystyle C^{r}} -ness of Φ {\displaystyle...

the components of a tensor, but under general coordinate transformations (diffeomorphisms) they do not. Most of the algebraic properties of the Christoffel...

that direction. This type of mapping is also called shear transformation, transvection, or just shearing. The transformations can be applied with a shear...

being either geometric transformations – transformation of the geographic element – or attribute transformations – transformations of the related attribute...

automorphism of a set. In geometry, isomorphisms and automorphisms are often called transformations, for example rigid transformations, affine transformations, projective...

defined as a set of d coordinates q = ( q 1 , q 2 , … , q d ) {\displaystyle \mathbf {q} =(q^{1},q^{2},\dots ,q^{d})} in which the coordinate hypersurfaces...

Herriott RM (July 1961). "Studies on transformations of Hemophilus influenzae. I. Competence". The Journal of General Physiology. 44 (6): 1201–27. doi:10...