Jacobi may refer to:

People

* Jacobi (surname), a list of people with the surname * Jacobi Boykins (born 1995), American basketball player * Jacobi Francis (born 1998), American football player * Jacobi Mitchell (born 1986), Bahamian sprinter * Jacobi Robinson (born 1984), Bermudian cricketer

In mathematics

Concepts named after the German mathematician Carl Gustav Jacob Jacobi: *

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, a method for determining the solutions of a diagonally dominant system of linear equations * Jacobi eigenvalue algorithm, 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, as well as in the design of electronic elliptic filters. While trigonometric functions are define ...

, a set of doubly-periodic functions *

Jacobian matrix and determinant In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals the number of compon ...

of a smooth map between Euclidean spaces or smooth manifolds *

Jacobi operator A Jacobi operator, also known as Jacobi matrix, is a symmetric linear operator acting on sequences which is given by an infinite tridiagonal matrix. It is commonly used to specify systems of orthonormal polynomials over a finite, positive Borel me ...

(Jacobi matrix), a tridiagonal symmetric matrix appearing in the theory of orthogonal polynomials *

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 of an odd prime number ''p'': its value at a (nonzero) quadratic residue mod ''p'' is 1 and at a non-quadratic re ...

* 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 associ ...

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 matr ...

for the derivative of the determinant of a matrix *

Jacobi triple product In mathematics, the Jacobi triple product is the 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'' ≠ 0. It ...

, 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. Theta functions are parametrized by points in a tube ...

s * Jacobi's theorem (disambiguation), several theorems

Other uses

* Jacobi Medical Center, New York * Jacobi (grape), 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 diam ...

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

People

In mathematics

Other uses

See also