Search results
Results From The WOW.Com Content Network
In mathematics, the Jacobi identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple product
There are several closely related functions called Jacobi theta functions, and many different and incompatible systems of notation for them. One Jacobi theta function (named after Carl Gustav Jacob Jacobi) is a function defined for two complex variables z and τ, where z can be any complex number and τ is the half-period ratio, confined to the upper half-plane, which means it has a positive ...
Jacobi was born of Ashkenazi Jewish parentage in Potsdam on 10 December 1804. He was the second of four children of a banker, Simon Jacobi. His elder brother, Moritz, would also become known later as an engineer and physicist. He was initially home schooled by his uncle Lehman, who instructed him in the classical languages and elements of ...
In mathematics, a Lie algebra (pronounced / l iː / LEE) is a vector space together with an operation called the Lie bracket, an alternating bilinear map, that satisfies the Jacobi identity. In other words, a Lie algebra is an algebra over a field for which the multiplication operation (called the Lie bracket) is alternating and satisfies the ...
Jacobi coordinates, a simplification of coordinates for an n-body system; Jacobi identity for non-associative binary operations; Jacobi's formula for the derivative of the determinant of a matrix; Jacobi triple product, an identity in the theory of theta functions; Jacobi's theorem (disambiguation), several theorems
In Lie algebras, the multiplication satisfies Jacobi identity instead of the associative law; this allows abstracting the algebraic nature of infinitesimal transformations. Other examples are quasigroup, quasifield, non-associative ring, and commutative non-associative magmas.
In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. ... (Jacobi identity) For all x in E i, ...
In mathematics, the Jacobi–Anger expansion (or Jacobi–Anger identity) is an expansion of exponentials of trigonometric functions in the basis of their harmonics. It is useful in physics (for example, to convert between plane waves and cylindrical waves), and in signal processing (to describe FM signals).