isometry's Usage Examples:

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

And if one isometry cannot change distance, neither can two (or three, or more) in succession; thus the composition of two isometries is again an isometry, and the set of isometries is closed under composition.

A random isometry, like taking a sheet of paper from a table and randomly laying it back, almost surely is a rotation or a glide reflection (they have three degrees of freedom).

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

This can be seen by considering a geodesic \gamma:[0,2]\to M from p to q and taking the isometry which fixes \gamma(1) and maps \gamma'(1) to -\gamma'(1).

Notable people with the surname include:François BoitardLouis Peter BoitardLouise BoitardPierre Boitard 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 properties such as length.

Alternatively, there is an isometry scalar matrix {uij}ij ∈ Cnm × nm such that A i ∑ j 1 u i j B j .

An isometry is completely determined by its effect on three independent (not collinear) points.

There is one further type of isometry, called a glide reflection (see below under classification of Euclidean plane isometries).

a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2).

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

The isometry group acts 'transitively' (since we can translate in t,y,z, and using the fourth vector we can move along x as well), so the spacetime is 'homogeneous'.

It can be shown that the Gödel solution is, up to local isometry, the only perfect fluid solution of the Einstein field equation admitting a five-dimensional Lie algebra of Killing vectors.

Synonyms:

equality,

Antonyms:

hardware, inequality,