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  2. Operation (mathematics) - Wikipedia

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

    [6] [7] [8] Operations on functions include composition and convolution. [9] [10] Operations may not be defined for every possible value of its domain. For example, in the real numbers one cannot divide by zero [11] or take square roots of negative numbers. The values for which an operation is defined form a set called its domain of definition ...

  3. Six operations - Wikipedia

    en.wikipedia.org/wiki/Six_operations

    In mathematics, Grothendieck's six operations, named after Alexander Grothendieck, is a formalism in homological algebra, also known as the six-functor formalism. [1] It originally sprang from the relations in étale cohomology that arise from a morphism of schemes f : X → Y .

  4. Positive operator - Wikipedia

    en.wikipedia.org/wiki/Positive_operator

    In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator acting on an inner product space is called positive-semidefinite (or non-negative) if, for every ⁡ (), , and , , where ⁡ is the domain of .

  5. Self-adjoint operator - Wikipedia

    en.wikipedia.org/wiki/Self-adjoint_operator

    In mathematics, a self-adjoint operator on a complex vector space V with inner product , is a linear map A (from V to itself) that is its own adjoint. That is, A x , y = x , A y {\displaystyle \langle Ax,y\rangle =\langle x,Ay\rangle } for all x , y {\displaystyle x,y} ∊ V .

  6. List of mathematical functions - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_functions

    In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. This is a listing of articles which explain some of these functions in more detail.

  7. Unbounded operator - Wikipedia

    en.wikipedia.org/wiki/Unbounded_operator

    The class of self-adjoint operators is especially important in mathematical physics. Every self-adjoint operator is densely defined, closed and symmetric. The converse holds for bounded operators but fails in general. Self-adjointness is substantially more restricting than these three properties.

  8. Idempotence - Wikipedia

    en.wikipedia.org/wiki/Idempotence

    Pressing the On button (green) is an idempotent operation, since it has the same effect whether done once or multiple times. Likewise, pressing Off is idempotent. 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 ...

  9. Function composition - Wikipedia

    en.wikipedia.org/wiki/Function_composition

    If an airplane's altitude at time t is a(t), and the air pressure at altitude x is p(x), then (p ∘ a)(t) is the pressure around the plane at time t. Function defined on finite sets which change the order of their elements such as permutations can be composed on the same set, this being composition of permutations.

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