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.
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 ?
D is a Banach algebra isometric isomorphism between M(H) and M with [D.sup.-1] = I.
The map [phi] : [S.sub.[alpha],[beta];[phi]] [right arrow] F(H) defined by [phi]([F.sup.[mu]]) = F([sigma]) = [F.sup.[mu]][|.sub.H] for [mu] [member of] M, where [sigma] = I[mu] [member of] M(H), is an isometric isomorphism as Banach algebras.
By Theorem 13, the map [[phi].sub.1] : [S.sub.[alpha],[beta];[phi]] [right arrow] M defined by [[phi].sub.1]([F.sup.[mu]]) = [mu], is an isometric isomorphism between Banach algebras.