isometry's Usage Examples:

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

} An isometry of Euclidean vector spaces is a linear isomorphism.

An isometry f : E → F {\displaystyle f\colon E\to F}.

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.

For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space.

T : V → V′ (isometry) such that Q ( v ) = Q ′ ( T v )  for all  v ∈ V .

} The isometry classes of n-dimensional.

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

In mathematics, the isometry group of a metric space is the set of all bijective isometries (i.

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

The compact real form of F4 is the isometry group of a 16-dimensional Riemannian manifold known as the octonionic projective.

indirect isometry; i.

An indirect isometry is an affine.

defines an isometry.

The other condition, UU* = I, defines a coisometry.

Thus a unitary operator is a bounded linear operator which is both an isometry and a.

With this distance, the set of isometry classes of n {\displaystyle n} -dimensional normed spaces becomes a compact.

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

Hilbert spaces is a canonical factorization as the product of a partial isometry and a non-negative operator.

automorphism group of the space X – here "automorphism group" can mean isometry group, diffeomorphism group, or homeomorphism group.

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.

vertices" means that each two vertices are symmetric to each other: A global isometry of the entire solid takes one vertex to the other while laying the solid.

If geometry is regarded as the study of isometry groups then a center is a fixed point of all the isometries which move the object onto itself.

Synonyms:

equality;

Antonyms:

hardware; inequality;