Linear Functional - Examples and Applications - Integration


Linear functionals first appeared in functional analysis, the study of vector spaces of functions. A typical example of a linear functional is integration: the linear transformation defined by the Riemann integral

is a linear functional from the vector space C of continuous functions on the interval to the real numbers. The linearity of I(ƒ) follows from the standard facts about the integral:

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Famous quotes containing the word integration:

    The more specific idea of evolution now reached is—a change from an indefinite, incoherent homogeneity to a definite, coherent heterogeneity, accompanying the dissipation of motion and integration of matter.
    Herbert Spencer (1820–1903)

    The only phenomenon with which writing has always been concomitant is the creation of cities and empires, that is the integration of large numbers of individuals into a political system, and their grading into castes or classes.... It seems to have favored the exploitation of human beings rather than their enlightenment.
    Claude Lévi-Strauss (b. 1908)

    Look back, to slavery, to suffrage, to integration and one thing is clear. Fashions in bigotry come and go. The right thing lasts.
    Anna Quindlen (b. 1952)