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

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

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...

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...

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...

matrix and determinant of a smooth map between Euclidean spaces or smooth manifolds Jacobi operator (Jacobi matrix), a tridiagonal symmetric matrix appearing...

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...

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...

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

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...

Carl Gustav Jacob Jacobi (/dʒəˈkoʊbi/; German: [jaˈkoːbi]; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions...

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....

Cayley–Hamilton theorem Cramer's rule Trace diagram Jacobi's formula Faddeev–LeVerrier algorithm Compound matrix Gantmacher, F. R. (1960). The Theory of Matrices...

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

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

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...

&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...

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...

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

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

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

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

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...

the following. The Jacobi method can be represented in matrix form as a splitting The Gauss–Seidel method can be represented in matrix form as a splitting...

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

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

algorithm. It follows that we need only prove the VD property for a Jacobi matrix. The blocks of Dirichlet-to-Neumann maps of planar graphs have the variation...

= ( 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...

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...

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