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  2. Convex conjugate - Wikipedia

    en.wikipedia.org/wiki/Convex_conjugate

    In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel transformation , Fenchel transformation , or Fenchel conjugate (after Adrien-Marie Legendre and Werner Fenchel ).

  3. Complex conjugate - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate

    In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, if a {\displaystyle a} and b {\displaystyle b} are real numbers, then the complex conjugate of a + b i {\displaystyle a+bi} is a − b i . {\displaystyle a-bi.}

  4. Wirtinger derivatives - Wikipedia

    en.wikipedia.org/wiki/Wirtinger_derivatives

    In complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators [1]), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives ...

  5. Conjugate element (field theory) - Wikipedia

    en.wikipedia.org/wiki/Conjugate_element_(field...

    In mathematics, in particular field theory, the conjugate elements or algebraic conjugates of an algebraic element α, over a field extension L/K, are the roots of the minimal polynomial p K,α (x) of α over K. Conjugate elements are commonly called conjugates in contexts where this is not ambiguous.

  6. Treatise on Analysis - Wikipedia

    en.wikipedia.org/wiki/Treatise_on_analysis

    The first volume was originally a stand-alone graduate textbook with a different title. It was first written in English and later translated into French, unlike the other volumes which were first written in French. It has been republished several times and is much more common than the later volumes of the series. The contents include Chapter I ...

  7. Éléments de mathématique - Wikipedia

    en.wikipedia.org/wiki/Éléments_de_mathématique

    Éléments de mathématique (English: Elements of Mathematics) is a series of mathematics books written by the pseudonymous French collective Nicolas Bourbaki. Begun in 1939, the series has been published in several volumes, and remains in progress. The series is noted as a large-scale, self-contained, formal treatment of mathematics. [1] [2]

  8. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    Marston Morse applied calculus of variations in what is now called Morse theory. [6] Lev Pontryagin, Ralph Rockafellar and F. H. Clarke developed new mathematical tools for the calculus of variations in optimal control theory. [6] The dynamic programming of Richard Bellman is an alternative to the calculus of variations. [7] [8] [9] [c]

  9. Complex conjugate of a vector space - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate_of_a...

    Thus, the complex conjugate to a vector , particularly in finite dimension case, may be denoted as † (v-dagger, a row vector that is the conjugate transpose to a column vector ). In quantum mechanics , the conjugate to a ket vector | ψ {\displaystyle \,|\psi \rangle } is denoted as ψ | {\displaystyle \langle \psi |\,} – a bra vector (see ...