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...

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

Jacobi identity. In analytical mechanics, the Jacobi identity is satisfied by the Poisson brackets. In quantum mechanics, it is satisfied by operator...

Riemannian manifold in which the characteristic polynomial of the Jacobi operator of unit tangent vectors is a constant on the unit tangent bundle. It...

by the Jacobi operator. When the polynomials are orthogonal on some region of the complex plane (viz, in Bergman space), the Jacobi operator is replaced...

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

method Jacobi method for complex Hermitian matrices Jacobi multiplier Jacobi operator Jacobi polynomials Continuous q-Jacobi polynomials Big q-Jacobi polynomials...

the study of Lie groups, a Dunkl operator is a certain kind of mathematical operator, involving differential operators but also reflections in an underlying...

transfer operator can likewise usually be interpreted as a right-shift. Particularly well studied right-shifts include the Jacobi operator and the Hessenberg...

smooth manifolds Jacobi operator (Jacobi matrix), a tridiagonal symmetric matrix appearing in the theory of orthogonal polynomials Jacobi polynomials, a...

The Hessenberg operator is an infinite dimensional Hessenberg matrix. It commonly occurs as the generalization of the Jacobi operator to a system of orthogonal...

parameters of the polynomial distribution approximation. Cauchy matrix Jacobi operator Toeplitz matrix, an "upside down" (that is, row-reversed) Hankel matrix...

theorem is named after Harald Cramér and Herman Ole Andreas Wold. Jacobi operator D. H. Fremlin, 2000. Measure Theory Archived 2010-11-01 at the Wayback...

can be solved by virtue of the inverse scattering transform for the Jacobi operator L. The main result implies that arbitrary (sufficiently fast) decaying...

only if) the numbers cn are real and the numbers dn are positive. Jacobi operator James Alexander Shohat Jean Favard Chihara, Theodore Seio (1978), An...

The Hamilton-Jacobi-Bellman (HJB) equation is a nonlinear partial differential equation that provides necessary and sufficient conditions for optimality...

of his thesis supervised by Fritz Gesztesy was Spectral Theory for Jacobi Operators (1995). After a postdoctoral position at the Rheinisch-Westfälischen...

In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential...

Gustav Jacob Jacobi in 1841, whose usage became widely adopted. The symbol is variously referred to as "partial", "curly d" or "Jacobi's delta", or as...

similar. The trace is 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 ⁡...

In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string...

related functions called Jacobi theta functions, and many different and incompatible systems of notation for them. One Jacobi theta function (named after...

This amounts to choosing an axis vector for the rotations; the defining Jacobi identity is a well-known property of cross products. The earliest 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. If...

Hamilton–Jacobi PDEs". arXiv:2202.11014 [math.OC]. Osher, Stanley; Heaton, Howard; Fung, Samy Wu (2023). "A Hamilton–Jacobi-based proximal operator". Proceedings...

bracket of vector fields, also known as the Jacobi–Lie bracket or the commutator of vector fields, is an operator that assigns to any two vector fields X...

perturbation V {\displaystyle V} . Similar inequalities can be proved for Jacobi operators. Lieb, Elliott H.; Thirring, Walter E. (1991). "Inequalities for the...

Dunkl operator, Jacobi–Dunkl operator, Dunkl–Cherednik operator Dickman–de Bruijn function Engel: Engel expansion Erdélyi Artúr: Erdelyi–Kober operator Leonhard...

referred to simply as the Jacobian. They are named after Carl Gustav Jacob Jacobi. The Jacobian matrix is the natural generalization to vector valued functions...

In the theory of many-particle systems, Jacobi coordinates often are used to simplify the mathematical formulation. These coordinates are particularly...