Jacobi matrix may refer to: Jacobian matrix and determinant of a smooth map between Euclidean spaces or smooth manifolds Jacobi operator (Jacobi matrix)...

matrix and (if applicable) the determinant are often referred to simply as the Jacobian in literature. They are named after Carl Gustav Jacob Jacobi....

attached to matrices (see above). Another matrix frequently used in geometrical situations is the Jacobi matrix of a differentiable map f : R n → R m ....

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...

stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi. Let A x = b {\displaystyle...

b_{i}=c_{i}=1} . Note: no boundary conditions are used here. Pentadiagonal matrix Jacobi matrix (operator) Thomas Muir (1960). A treatise on the theory of determinants...

algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process...

upper Hessenberg. A matrix that is both upper Hessenberg and lower Hessenberg is a tridiagonal matrix, of which the Jacobi matrix is an important example...

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....

related to the derivative of the determinant (see Jacobi's formula). The trace of an n × n square matrix A is defined as: 34  tr ⁡ ( A ) = ∑ i = 1 n a i...

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 identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple...

M} . Two-sided Jacobi SVD algorithm—a generalization of the Jacobi eigenvalue algorithm—is an iterative algorithm where a square matrix is iteratively...

classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though that...

= ( D − L ) − 1 U {\displaystyle T_{1}=(D-L)^{-1}U} be the matrix splitting for the Jacobi method and the Gauss-Seidel method respectively. Theorem: If...

linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its negative. That is, it satisfies the...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are...

square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the...

they satisfy certain trace equalities. Canonical forms Matrix congruence Matrix equivalence Jacobi rotation Beauregard, Raymond A.; Fraleigh, John B. (1973)...

skew-symmetric matrix Jacobi's four-square theorem, in number theory Jacobi's theorem (geometry), on concurrent lines associated with any triangle Jacobi's theorem...

the operator: T ¯ {\displaystyle {\overline {T}}} has a tridiagonal Jacobi matrix representation. This in turn leads to a tridiagonal model of positive...

&0&1\end{bmatrix}}^{\mathsf {T}}} , and J is the following tridiagonal matrix, called the Jacobi matrix: J = [ a 0 1 0 ⋯ 0 b 1 a 1 1 ⋱ ⋮ 0 b 2 ⋱ ⋱ 0 ⋮ ⋱ ⋱ a n − 2...

elimination (LU factorization). The Jacobi and Gauss–Seidel methods for solving a linear system converge if the matrix is strictly (or irreducibly) diagonally...

In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from...

Magnus series gives the solution as an infinite sum. By Jacobi's formula, for any complex square matrix the following trace identity holds: det ( e A ) = e...

Jacobi symbol Jacobi theta function Jacobi zeta function Jacobi's theorem (skew-symmetric matrix) Jacobi transform Jacobi triple product Jacobi-type J-fractions...

In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics...

formula, also known as the Abel–Jacobi–Liouville identity, is an equation that expresses the determinant of a square-matrix solution of a first-order system...

In mathematics, the Abel–Jacobi map is a construction of algebraic geometry which relates an algebraic curve to its Jacobian variety. In Riemannian geometry...