# isometry

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## isometry

[ī′säm·ə·trē]
(mathematics)
A mapping ƒ from a metric space X to a metric space Y where the distance between any two points of X equals the distance between their images under ƒ in Y.
A linear isomorphism σ of a vector space E onto itself such that, for a given bilinear form g, gx, σ y)= g (x,y) for all x and y in E.

## isometry

(mathematics)
A mapping of a metric space onto another or onto itself so that the distance between any two points in the original space is the same as the distance between their images in the second space. For example, any combination of rotation and translation is an isometry of the plane.
References in periodicals archive ?
then the Cauchy sequence [([[~.T].sub.n]).sub.n = 1.sup.[infinity]] convergent to some linear isometry [~.T].
Moreover [Mathematical Expression Omitted] is an isometry from [Mathematical Expression Omitted] to [Mathematical Expression Omitted] and [Mathematical Expression Omitted] from [Mathematical Expression Omitted] to [Mathematical Expression Omitted].
* General relativistic theories: the isometry group.
We have filled out the diagonal of U to make it an isometry.
Regression analysis for the log of lower leg length relative to the log of the femur length, differences respect to isometry (slope value equal 1) and slope homogeneity test with respect to theropods.
Cartan in  showed that the examples above cover, in fact, all possible 3-dimensional homogeneous spaces with 4-dimensional isometry group.
Thus [mathematical expression not reproducible] Jarosz  and Jarosz and Pathak  studied ||/ ||o([0>1]).) Jarosz  and Jarosz and Pathak  studied a problem when an isometry on a space of continuous functions is a weighted composition operator.
Let X be the Hardy space [H.sup.p] or the Bergman space [L.sup.p.sub.a] (1 < p < [infinity], p [not equal to] 2) and T = [mu][([phi]').sup.[beta]][C.sub.[phi]] be a surjective linear isometry on X for some [phi] [member of] Aut(D) and |[mu]| = 1 where [beta] = [1/p] for the space [H.sup.p] and [beta] = [2/p] for the space [L.sup.p.suba.].If T is weakly supercyclic then [phi] is not an elliptic automorphism.
Using the isometry property (8) of the stochastic integral and (28), we have
One of the most commonly known conditions is the restricted isometry property (RIP).
Since the entries of [PHI]D are correlated when D is highly coherent, [PHI]D may no longer satisfy the standard restricted isometry property (RIP ) and the mutual incoherence property (MIP ) which are commonly used in the standard CS framework.
However, the CS-based broadband channel estimation is more complex than the SAF algorithms because the CS-based channel estimations require measurement matrix construction which is bounded by restricted isometry property .

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