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  2. Contraction mapping - Wikipedia

    en.wikipedia.org/wiki/Contraction_mapping

    A contraction mapping has at most one fixed point. Moreover, the Banach fixed-point theorem states that every contraction mapping on a non-empty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x , f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.

  3. Contraction (operator theory) - Wikipedia

    en.wikipedia.org/wiki/Contraction_(operator_theory)

    This notion is a special case of the concept of a contraction mapping, but every bounded operator becomes a contraction after suitable scaling. The analysis of contractions provides insight into the structure of operators, or a family of operators. The theory of contractions on Hilbert space is largely due to Béla SzĹ‘kefalvi-Nagy and Ciprian ...

  4. Contraction - Wikipedia

    en.wikipedia.org/wiki/Contraction

    Edge contraction or vertex contraction, graph operations used in graph theory; Tensor contraction, an operation on one or more tensors that arises from the natural pairing of a finite-dimensional vector space and its dual; Left contraction and right contraction of multivectors in a geometric algebra, extensions of the inner product

  5. Wikipedia:List of English contractions - Wikipedia

    en.wikipedia.org/wiki/Wikipedia:List_of_English...

    Some acronyms are formed by contraction; these are covered at Wikipedia:Manual of Style/Abbreviations. Some trademarks (e.g. Nabisco) and titles of published works (e.g. “Ain't That a Shame”) consist of or contain contractions; these are covered at Wikipedia:Manual of Style/Trademarks and Wikipedia:Manual of Style/Titles, respectively.

  6. Seventh grade - Wikipedia

    en.wikipedia.org/wiki/Seventh_grade

    Seventh grade (also 7th Grade or Grade 7) is the seventh year of formal or compulsory education. The seventh grade is typically the first or second year of middle school. In the United States, kids in seventh grade are usually around 12–13 years old. Different terms and numbers are used in other parts of the world.

  7. Contraction theorem - Wikipedia

    en.wikipedia.org/wiki/Contraction_theorem

    In mathematics contraction theorem may refer to: The Banach contraction mapping theorem in functional analysis; Castelnuovo's contraction theorem in algebraic geometry

  8. Length contraction - Wikipedia

    en.wikipedia.org/wiki/Length_contraction

    Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, ...

  9. Edge contraction - Wikipedia

    en.wikipedia.org/wiki/Edge_contraction

    Edge contraction is used in the recursive formula for the number of spanning trees of an arbitrary connected graph, [7] and in the recurrence formula for the chromatic polynomial of a simple graph. [8] Contractions are also useful in structures where we wish to simplify a graph by identifying vertices that represent essentially equivalent entities.

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