isometry

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“
The image V of this isometry is the smallest closed subspace of H that contains Note the contrast here between conditional and unconditional summability (which needs only square-summability of the coefficients are absolutely summable).

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Definitions (7)

Toggle American Heritage definitions American Heritage Dictionary (3)

  1. noun Equality of measure.
  2. noun Equality of elevation above sea level.
  3. noun Mathematics A function between metric spaces which preserves distances, such as a rotation or translation in a plane.

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Examples (14)

  • : A transformation which preserves the geometrical properties of the Euclidean spacea distance-preserving mapping or isometry. —  Citizendium, the Citizens' Compendium - Recent changes [en]
  • Restricted isometry properties and nonconvex compressive sensing —  CiteULike: Everyone's library
  • It was also shown that a weaker restricted isometry property is sufficient to guarantee perfect recovery in the p case. —  CiteULike: Everyone's library
  • In this work, we generalize this result to an p variant of the restricted isometry property, and then determine how many random, Gaussian measurements are sufficient for the condition to hold with high probability. —  CiteULike: Everyone's library
  • Inspired by the above exercise, we say that two inner product spaces are isomorphic if there exists an invertible isometry from one space to the other; such invertible isometries are known as isomorphisms. —  What's new
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