"Jacobi matrix (operator)" redirects here. For a similar term, see Jacobian matrix.
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 measure. This operator is named after Carl Gustav Jacob Jacobi.
The name derives from a theorem from Jacobi, dating to 1848, stating that every symmetric matrix over a principal ideal domain is congruent to a tridiagonal matrix.
A Jacobioperator, 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...
Jacobi matrix may refer to: Jacobian matrix and determinant of a smooth map between Euclidean spaces or smooth manifolds Jacobioperator (Jacobi matrix)...
by the Jacobioperator. When the polynomials are orthogonal on some region of the complex plane (viz, in Bergman space), the Jacobioperator is replaced...
transfer operator can likewise usually be interpreted as a right-shift. Particularly well studied right-shifts include the Jacobioperator and the Hessenberg...
The Hessenberg operator is an infinite dimensional Hessenberg matrix. It commonly occurs as the generalization of the Jacobioperator to a system of orthogonal...
parameters of the polynomial distribution approximation. Cauchy matrix Jacobioperator Toeplitz matrix, an "upside down" (that is, row-reversed) Hankel matrix...
the study of Lie groups, a Dunkl operator is a certain kind of mathematical operator, involving differential operators but also reflections in an underlying...
theorem is named after Harald Cramér and Herman Ole Andreas Wold. Jacobioperator D. H. Fremlin, 2000. Measure Theory Archived 2010-11-01 at the Wayback...
of his thesis supervised by Fritz Gesztesy was Spectral Theory for JacobiOperators (1995). After a postdoctoral position at the Rheinisch-Westfälischen...
can be solved by virtue of the inverse scattering transform for the Jacobioperator L. The main result implies that arbitrary (sufficiently fast) decaying...
Hamilton's principle Hamilton–Jacobi equation Hamilton–Jacobi–Bellman equation, related equation in control theory Hamilton–Jacobi–Einstein equation In both...
In the theory of many-particle systems, Jacobi coordinates often are used to simplify the mathematical formulation. These coordinates are particularly...
bracket, forms a Lie algebra, and so it is anti-symmetric, and obeys the Jacobi identity. The Poisson bracket acts as a derivation of the associative product...
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...
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...
the dynamics of a system. There are other formulations such as Hamilton–Jacobi theory, Routhian mechanics, and Appell's equation of motion. All equations...
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