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  2. Idempotence - Wikipedia

    en.wikipedia.org/wiki/Idempotence

    Idempotence (UK: / ˌ ɪ d ɛ m ˈ p oʊ t ən s /, [1] US: / ˈ aɪ d ə m-/) [2] is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application.

  3. Idempotent matrix - Wikipedia

    en.wikipedia.org/wiki/Idempotent_matrix

    An idempotent matrix is always diagonalizable. [3] Its eigenvalues are either 0 or 1: if is a non-zero eigenvector of some idempotent matrix and its associated eigenvalue, then = = = = =, which implies {,}.

  4. Idempotent relation - Wikipedia

    en.wikipedia.org/wiki/Idempotent_relation

    Definition. As a shorthand, ... Because idempotence incorporates both transitivity and the second property above, it is a stronger property than transitivity.

  5. Idempotent (ring theory) - Wikipedia

    en.wikipedia.org/wiki/Idempotent_(ring_theory)

    In ring theory, a branch of mathematics, an idempotent element or simply idempotent of a ring is an element a such that a 2 = a. [1] [a] That is, the element is idempotent under the ring's multiplication.

  6. Side effect (computer science) - Wikipedia

    en.wikipedia.org/wiki/Side_effect_(computer_science)

    Idempotence. A subroutine with side effects is idempotent if multiple applications of the subroutine have the same effect on the system state as a single ...

  7. Band (algebra) - Wikipedia

    en.wikipedia.org/wiki/Band_(algebra)

    The idempotents of a rectangular semigroup form a sub band that is a rectangular band but a rectangular semigroup may have elements that are not idempotent. In a band the second identity obviously implies the first but that requires idempotence. There exist semigroups that satisfy the second identity but are not bands and do not satisfy the first.

  8. Idempotency of entailment - Wikipedia

    en.wikipedia.org/wiki/Idempotency_of_entailment

    Idempotency of entailment is a property of logical systems that states that one may derive the same consequences from many instances of a hypothesis as from just one. This property can be captured by a structural rule called contraction, and in such systems one may say that entailment is idempotent if and only if contraction is an admissible rule.

  9. Projection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Projection_(mathematics)

    In this case, idempotent means that projecting twice is the same as projecting once. The restriction to a subspace of a projection is also called a projection, even if the idempotence property is lost. An everyday example of a projection is the casting of shadows onto a plane (sheet of paper): the projection of a point is its shadow on the ...