isometry

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Related to Isometric mapping: isometry

isometry

(ī-sŏm′ĭ-trē)
n.
1. Equality of measure.
2. Equality of elevation above sea level.
3. Mathematics A function between metric spaces which preserves distances, such as a rotation or translation in a plane.
4. Biology A proportional change in the size of a part or parts of an organism as the organism grows.
The American Heritage® Medical Dictionary Copyright © 2007, 2004 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.
References in periodicals archive ?
Yao, "Data dimensionality reduction method of semi-supervised isometric mapping based on regularization," Journal of Electronics & Information Technology, vol.
where sm.[[S.sub.1](E)] is the set of all the smooth points of [S.sub.1](E), then [V.sub.0] can be extended to be an isometric mapping defined on the whole space.
If [V.sub.0] is an isometric mapping from the unit sphere [S.sub.1][[l.sup.p([GAMMA])] into [S.sub.1][[l.sup.p([DELTA])] for p > 1, then [V.sub.0] can be extended to a linear isometry if and only if for each x [member of] [S.sub.1][[l.sup.p([GAMMA])] and [gamma] [member of] [GAMMA] there exists a real number [[eta].sub.[gamma]] such that [V.sub.0](x)|supp.([V.sub.0]([e.sub.[gamma]])) = [[eta].sub.[gamma]][V.sub.0]([e.sub.[gamma]]).
From this definition, Yang showed that any into isometric mapping between the unit sphere of [L.sup.p]([mu]) and the unit sphere of [L.sup.p]([nu], H) (where, 1 < p [not equal to] 2 and H is a Hilbert space) can be extended to be a real linear isometry on the whole space.