# isometry

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## 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.
References in periodicals archive ?
Now the operator [mathematical expression not reproducible] onto [([L.sub.2](R)).sup.n], and its restriction to [F.sup.2.sub.n] (C) is an isometric isomorphism. Furthermore, the adjoint operator [R.sup.*.sub.n] = U* [R.sub.0,n] is an isometric isomorphism from [([L.sup.2](R)).sup.n] onto the space [F.sup.2.sub.n] (C).
As above, the map [LAMBDA] : [M.sub.a][(S, [omega]).sup.*] [right arrow] M([M.sub.a](S, [omega]), [M.sub.a][(S, [omega]).sup.*]) given by [LAMBDA](f) = [[lambda].sub.f], is an isometric isomorphism. Now we consider P : [M.sub.a][(S, [omega]).sup.*] [right arrow] [M.sub.a][(S, [omega]).sup.*] defined by P(f) = [[LAMBDA].sup-1] (Q([LAMBDA](f))).
Using the isometric isomorphisms between [H.sup.s] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], we see that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
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