isometry

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Related to Isometric mapping: isometry

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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

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.
This article is provided by FOLDOC - Free Online Dictionary of Computing (foldoc.org)
References in periodicals archive ?
Let [V.sub.0] be an isometric mapping from the unit sphere [S.sub.1][[L.sup.1]([mu])] into the unit sphere [S.sub.1](E) of a Banach space E, then [V.sub.0] can be extended to a (real) linear isometry defined on the whole space [L.sup.1]([mu]) if and only if the following condition holds:
That is, if [OMEGA] is a compact Hausdorff space and E is a real Banach space, suppose that [V.sub.0] is an isometric mapping from [S.sub.1][C([OMEGA])] into [S.sub.1](E), then, for every t [member of] [OMEGA], there exists an [f.sub.t] [member of] E* such that ||[f.sub.t]|| = 1 and
Ding, The representation theorem of onto isometric mapping between two unit spheres of [l.sup.1]([GAMMA])-type spaces and the application on isometric extension problem, Acta Math.
Banach (4) got some representation theorem for isometric mappings V [member of] B(c) and V [member of] B([l.sup.p]) for p [greater than or equal to] 1.