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multiplicity of root

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  • Multiplicity (mathematics) — In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial equation has a root at a given point. The notion of multiplicity is important to be… …   Wikipedia

  • Root-finding algorithm — A root finding algorithm is a numerical method, or algorithm, for finding a value x such that f(x) = 0, for a given function f. Such an x is called a root of the function f. This article is concerned with finding scalar, real or complex roots,… …   Wikipedia

  • Root of unity — The 5th roots of unity in the complex plane In mathematics, a root of unity, or de Moivre number, is any complex number that equals 1 when raised to some integer power n. Roots of unity are used in many branches of mathematics, and are especially …   Wikipedia

  • multiplicity — noun (plural ties) Etymology: Middle English, from Middle French multiplicité, from Late Latin multiplicitat , multiplicitas, from Latin multiplic , multiplex Date: 15th century 1. a. the quality or state of being multiple or various b. the… …   New Collegiate Dictionary

  • Unit root — In time series models in econometrics, a linear stochastic process has a unit root if 1 is a root of the process s characteristic equation. The process will be non stationary. If the other roots of the characteristic equation lie inside the unit… …   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

  • KABBALAH — This entry is arranged according to the following outline: introduction general notes terms used for kabbalah the historical development of the kabbalah the early beginnings of mysticism and esotericism apocalyptic esotericism and merkabah… …   Encyclopedia of Judaism

  • Newton's method — In numerical analysis, Newton s method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real valued function. The… …   Wikipedia

  • Idealism (italian) and after — Italian idealism and after Gentile, Croce and others Giacomo Rinaldi INTRODUCTION The history of twentieth century Italian philosophy is strongly influenced both by the peculiar character of its evolution in the preceding century and by… …   History of philosophy

  • Dynkin diagram — See also: Coxeter–Dynkin diagram Finite Dynkin diagrams Affine (extended) Dynkin diagrams …   Wikipedia

  • Discriminant — In algebra, the discriminant of a polynomial is an expression which gives information about the nature of the polynomial s roots. For example, the discriminant of the quadratic polynomial is Here, if Δ > 0, the polynomial has two real roots,… …   Wikipedia

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