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(continuous linear functional)

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  • Linear functional — This article deals with linear maps from a vector space to its field of scalars.  These maps may be functionals in the traditional sense of functions of functions, but this is not necessarily the case. In linear algebra, a linear functional… …   Wikipedia

  • Continuous linear operator — In functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed spaces is a bounded linear… …   Wikipedia

  • Continuous linear extension — In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space X by first defining a linear transformation on a dense subset of X and then extending to the whole space via the theorem below.… …   Wikipedia

  • Positive linear functional — In mathematics, especially in functional analysis, a positive linear functional on an ordered vector space ( V , ≤) is a linear functional f on V so that for all positive elements v of V , that is v ge;0, it holds that:f(v)geq 0.In other words, a …   Wikipedia

  • Functional analysis — For functional analysis as used in psychology, see the functional analysis (psychology) article. Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of vector spaces and operators acting upon… …   Wikipedia

  • Linear map — In mathematics, a linear map, linear mapping, linear transformation, or linear operator (in some contexts also called linear function) is a function between two vector spaces that preserves the operations of vector addition and scalar… …   Wikipedia

  • Continuous functions on a compact Hausdorff space — In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by C(X), is a vector… …   Wikipedia

  • Functional-theoretic algebra — In mathematics, a functional theoretic algebra is a unital associative algebra whose multiplication is defined by the action of two linear functionals.Let AF be a vector space over a field F , and let L 1 and L 2 be two linear functionals on AF… …   Wikipedia

  • Functional integration — You may also be looking for functional integration (neurobiology) or functional integration (sociology). Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space,… …   Wikipedia

  • Discontinuous linear map — In mathematics, linear maps form an important class of simple functions which preserve the algebraic structure of linear spaces and are often used as approximations to more general functions (see linear approximation). If the spaces involved are… …   Wikipedia

  • Functional decomposition — refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed (i.e., recomposed) from those parts by function composition. In general, this process of …   Wikipedia

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