In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed...

In mathematics, the isometry group of a metric space is the set of all bijective isometries (that is, bijective, distance-preserving maps) from the metric...

geometry) Isometry group Quasi-isometry Dade isometry Euclidean isometry Euclidean plane isometry Itō isometry Isometric (disambiguation) Isometries in physics...

In mathematics, a quasi-isometry is a function between two metric spaces that respects large-scale geometry of these spaces and ignores their small-scale...

mathematical functional analysis a partial isometry is a linear map between Hilbert spaces such that it is an isometry on the orthogonal complement of its kernel...

In mathematics, the Itô isometry, named after Kiyoshi Itô, is a crucial fact about Itô stochastic integrals. One of its main applications is to enable...

{1}{2}}\left(\|x+y\|^{2}-\|x\|^{2}-\|y\|^{2}\right).} An isometry of Euclidean vector spaces is a linear isomorphism. An isometry f : E → F {\displaystyle f\colon E\to F}...

In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space E n {\displaystyle \mathbb {E} ^{n}} ; that is, the transformations...

In geometry, a Euclidean plane isometry is an isometry of the Euclidean plane, or more informally, a way of transforming the plane that preserves geometrical...

In linear algebra, the restricted isometry property (RIP) characterizes matrices which are nearly orthonormal, at least when operating on sparse vectors...

If h is a translation, then its conjugation by an isometry can be described as applying the isometry to the translation: the conjugation of a translation...

A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set...

in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a...

isometric linear operators on a given Hilbert space. It states that every isometry is a direct sum of copies of the unilateral shift and a unitary operator...

rigid transformation (also called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the...

rotation-reflection, rotoreflection, rotary reflection, or rotoinversion) is an isometry in Euclidean space that is a combination of a rotation about an axis and...

In mathematical finite group theory, the Dade isometry is an isometry from class function on a subgroup H with support on a subset K of H to class functions...

drawings free of optical distortion. This would lead him to formulate isometry. Isometry means "equal measures" because the same scale is used for height,...

T : V → V′ (isometry) such that Q ( v ) = Q ′ ( T v )  for all  v ∈ V . {\displaystyle Q(v)=Q'(Tv){\text{ for all }}v\in V.} The isometry classes of n-dimensional...

at p. The lemma allows the exponential map to be understood as a radial isometry, and is of fundamental importance in the study of geodesic convexity and...

bijective distance-preserving function is called an isometry. One perhaps non-obvious example of an isometry between spaces described in this article is the...

For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups...

spacetime, i.e. they are isometries of Minkowski space. They are studied primarily in special relativity. Those isometries that leave the origin fixed...

orientation concept: an isometry is direct if and only if it is a product of squares of isometries, and if not, it is an indirect isometry. The resulting chirality...

Hilbert spaces is a canonical factorization as the product of a partial isometry and a non-negative operator. The polar decomposition for matrices generalizes...

(1759–1837), the concept of isometry had existed in a rough empirical form for centuries. From the middle of the 19th century, isometry became an "invaluable...

of the coordinate system. In a Euclidean space, any translation is an isometry. If v {\displaystyle \mathbf {v} } is a fixed vector, known as the translation...

discrete isometry group is an isometry group such that for every point of the metric space the set of images of the point under the isometries is a discrete...

not mapped to itself by point inversion. The regular tetrahedron has 24 isometries, forming the symmetry group Td, [3,3], (*332), isomorphic to the symmetric...

The isometry group of a uniformized Riemann surface (equivalently, the conformal automorphism group) reflects its geometry: genus 0 – the isometry group...