Jacobi matrix
Encyclopedia
Jacobi matrix may refer to:
- Jacobian matrix and determinant of a smooth map between Euclidean spaceEuclidean spaceIn mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions...
s or smooth manifolds - Jacobi matrixJacobi operatorA Jacobi operator, named after Carl Gustav Jakob Jacobi, is a symmetric linear operator acting on sequences which is given by a tridiagonal matrix in the standard basis given by Kronecker deltas.- Self-adjoint Jacobi operators :...
, a tridiagonal symmetric matrix appearing in the theory of orthogonal polynomialsOrthogonal polynomialsIn mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...