Jacobi may refer to: * People with the surname

Jacobi Jacobi may refer to: * People with the surname Jacobi (surname), Jacobi Mathematics: * Jacobi sum, a type of character sum * Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations * Jacobi eigenva ...

Mathematics: *

Jacobi sum In mathematics, a Jacobi sum is a type of character sum formed with Dirichlet characters. Simple examples would be Jacobi sums ''J''(''χ'', ''ψ'') for Dirichlet characters ''χ'', ''ψ'' modulo a prime number ''p'', defined by : J(\chi,\psi) = ...

, a type of character sum *

Jacobi method In numerical linear algebra, the Jacobi method is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The ...

, a method for determining the solutions of a diagonally dominant system of linear equations *

Jacobi eigenvalue algorithm In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization). It is named after Carl Gustav Jacob Jacobi, ...

, a method for calculating the eigenvalues and eigenvectors of a real symmetric matrix *

Jacobi elliptic functions In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While tri ...

, a set of doubly-periodic functions *

Jacobi polynomials In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P_n^(x) are a class of Classical orthogonal polynomials, classical orthogonal polynomials. They are orthogonal with respect to the weight (1-x)^\alpha(1+x)^\beta ...

, a class of orthogonal polynomials *

Jacobi symbol Jacobi symbol for various ''k'' (along top) and ''n'' (along left side). Only are shown, since due to rule (2) below any other ''k'' can be reduced modulo ''n''. Quadratic residues are highlighted in yellow — note that no entry with a ...

, a generalization of the

Legendre symbol In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo an odd prime number ''p'': its value at a (nonzero) quadratic residue mod ''p'' is 1 and at a non-quadratic residu ...

* Jacobi coordinates, a simplification of coordinates for an n-body system *

Jacobi identity 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, affects the result of the operation. By contrast, for operations with the asso ...

for non-associative binary operations *

Jacobi's formula In matrix calculus, Jacobi's formula expresses the derivative of the determinant of a matrix ''A'' in terms of the adjugate of ''A'' and the derivative of ''A''., Part Three, Section 8.3 If is a differentiable map from the real numbers to matri ...

for the derivative of the determinant of a matrix *

Jacobi triple product In mathematics, the Jacobi triple product is the mathematical identity: :\prod_^\infty \left( 1 - x^\right) \left( 1 + x^ y^2\right) \left( 1 +\frac\right) = \sum_^\infty x^ y^, for complex numbers ''x'' and ''y'', with , ''x'', < 1 and ''y ...

an identity in the theory of

theta function In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theo ...

s * Jacobi's theorem (disambiguation) (various) Other: *

Jacobi Medical Center Jacobi Medical Center (NYC Health + Hospitals/Jacobi) is a municipal hospital operated by NYC Health + Hospitals in affiliation with the Albert Einstein College of Medicine. The facility is located in the Morris Park neighborhood of the Bronx, Ne ...

, New York *

Jacobi (grape) Jacobi may refer to: * People with the surname Jacobi Mathematics: * Jacobi sum, a type of character sum * Jacobi method, a method for determining the solutions of a diagonally dominant system of linear equations * Jacobi eigenvalue algorithm, a ...

, another name for the French/German wine grape Pinot Noir Précoce *

Jacobi (crater) Jacobi is a lunar impact crater that is located in the southern highlands on the near side of the Moon. It lies southeast of the crater Lilius, with Cuvier to the north-northwest and Baco to the northeast. The crater is 68 kilometers in diamet ...

, a lunar impact crater in the southern highlands on the near side of the Moon * Software_for_handling_chess_problems#Jacobi, chess software

See also