complex conjugate

complex conjugate

English-Finnish mathematical dictionary. 2011.

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  • Complex conjugate — Geometric representation of z and its conjugate in the complex plane In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magni …   Wikipedia

  • complex conjugate — noun Of a complex number x, the complex number formed by changing the sign of the imaginary part: The complex conjugate of a + bi is a bi. Syn: conjugate …   Wiktionary

  • Complex conjugate vector space — In mathematics, the (formal) complex conjugate of a complex vector space is the complex vector space consisting of all formal complex conjugates of elements of . That is, is a vector space whose elements are in one to one correspondence with the… …   Wikipedia

  • Complex conjugate representation — In mathematics, if G is a group and ρ is a representation of it over the complex vector space V, then the complex conjugate representation ρ* is defined over the conjugate vector space V* as follows: ρ*(g) is the conjugate of ρ(g) for all g in G …   Wikipedia

  • Complex conjugate root theorem — In mathematics, the complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root… …   Wikipedia

  • complex conjugate matrix — kompleksiškai jungtinė matrica statusas T sritis fizika atitikmenys: angl. complex conjugate matrix vok. komplex konjugierte Matrix, f rus. комплексно сопряжённая матрица, f pranc. matrice complexe conjuguée, f …   Fizikos terminų žodynas

  • complex conjugate — noun either of two complex numbers whose real parts are identical and whose imaginary parts differ only in sign • Hypernyms: ↑complex number, ↑complex quantity, ↑imaginary number, ↑imaginary …   Useful english dictionary

  • Conjugate transpose — Adjoint matrix redirects here. For the classical adjoint matrix, see Adjugate matrix. In mathematics, the conjugate transpose, Hermitian transpose, Hermitian conjugate, or adjoint matrix of an m by n matrix A with complex entries is the n by m… …   Wikipedia

  • Complex number — A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the square root of –1. A complex… …   Wikipedia

  • Conjugate (algebra) — This article is about conjugates in field extensions. For other uses, see Conjugation. In algebra, a conjugate of an element in a quadratic extension field of a field K is its image under the unique non identity automorphism of the extended field …   Wikipedia

  • Conjugate gradient method — A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic,… …   Wikipedia

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