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Symmetric Positive Definite

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  • Positive-definite matrix — In linear algebra, a positive definite matrix is a matrix that in many ways is analogous to a positive real number. The notion is closely related to a positive definite symmetric bilinear form (or a sesquilinear form in the complex case). The… …   Wikipedia

  • Positive-definite function — In mathematics, the term positive definite function may refer to a couple of different concepts. Contents 1 In dynamical systems 2 In analysis 2.1 Bochner s theorem 2.1.1 Applications …   Wikipedia

  • Symmetric matrix — In linear algebra, a symmetric matrix is a square matrix, A , that is equal to its transpose:A = A^{T}. ,!The entries of a symmetric matrix are symmetric with respect to the main diagonal (top left to bottom right). So if the entries are written… …   Wikipedia

  • Definite quadratic form — In mathematics, a definite quadratic form is a real valued quadratic form over some vector space V that has the same sign (always positive or always negative) for every nonzero vector of V. The definite quadratic forms correspond in one to one… …   Wikipedia

  • Particle in a spherically symmetric potential — In quantum mechanics, the particle in a spherically symmetric potential describes the dynamics of a particle in a potential which has spherical symmetry. The Hamiltonian for such a system has the form:hat{H} = frac{hat{p}^2}{2m 0} + V(r)where m 0 …   Wikipedia

  • Cholesky decomposition — In linear algebra, the Cholesky decomposition or Cholesky triangle is a decomposition of a Hermitian, positive definite matrix into the product of a lower triangular matrix and its conjugate transpose. It was discovered by André Louis Cholesky… …   Wikipedia

  • Mercer's theorem — In mathematics, specifically functional analysis, Mercer s theorem is a representation of a symmetric positive definite function on a square as a sum of a convergent sequence of product functions. This theorem, presented in (Mercer 1909), is one… …   Wikipedia

  • List of numerical analysis topics — This is a list of numerical analysis topics, by Wikipedia page. Contents 1 General 2 Error 3 Elementary and special functions 4 Numerical linear algebra …   Wikipedia

  • Conjugate gradient method — A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic,… …   Wikipedia

  • Inner product space — In mathematics, an inner product space is a vector space with the additional structure of inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.… …   Wikipedia

  • Multivariate kernel density estimation — Kernel density estimation is a nonparametric technique for density estimation i.e., estimation of probability density functions, which is one of the fundamental questions in statistics. It can be viewed as a generalisation of histogram density… …   Wikipedia

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