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, g (σ x, 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.
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References in periodicals archive ?
then the Cauchy sequence [([[~.T].sub.n]).sub.n = 1.sup.[infinity]] convergent to some linear isometry [~.T].
On the isometric extension problem: a survey
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].
A compactness property for solutions of the Ricci flow
* General relativistic theories: the isometry group.
The lessons of the hole argument
We have filled out the diagonal of U to make it an isometry.
On the roots of linear transformations
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.
Are Cursorial Birds Good Kinematic Models of Non-Avian Theropods?/? Son los Pajaros Corredores Buenos Modelos Cinematicos de Teropodos No Aviares?
Cartan in [26] showed that the examples above cover, in fact, all possible 3-dimensional homogeneous spaces with 4-dimensional isometry group.
Willmore-Like Tori in Killing Submersions
Thus [mathematical expression not reproducible] Jarosz [5] and Jarosz and Pathak [6] studied ||/ ||o([0>1]).) Jarosz [5] and Jarosz and Pathak [6] studied a problem when an isometry on a space of continuous functions is a weighted composition operator.
Hermitian Operators and Isometries on Banach Algebras of Continuous Maps with Values in Unital Commutative C*-Algebras
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.
Non-Weakly Supercyclic Classes of Weighted Composition Operators on Banach Spaces of Analytic Functions
Using the isometry property (8) of the stochastic integral and (28), we have
Malliavin Differentiability of Solutions of SPDEs with Levy White Noise
One of the most commonly known conditions is the restricted isometry property (RIP).
Support Recovery of Greedy Block Coordinate Descent Using the Near Orthogonality Property
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 [1]) and the mutual incoherence property (MIP [17]) which are commonly used in the standard CS framework.
Improved RIP Conditions for Compressed Sensing with Coherent Tight Frames
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 [24].
Adaptive Channel Estimation Based on an Improved Norm-Constrained Set-Membership Normalized Least Mean Square Algorithm

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