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negative eigenvalue

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  • Eigenvalue, eigenvector and eigenspace — In mathematics, given a linear transformation, an Audio|De eigenvector.ogg|eigenvector of that linear transformation is a nonzero vector which, when that transformation is applied to it, changes in length, but not direction. For each eigenvector… …   Wikipedia

  • Eigenvalue algorithm — In linear algebra, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Contents 1 Characteristic polynomial 2 Power… …   Wikipedia

  • Jacobi eigenvalue algorithm — The Jacobi eigenvalue algorithm is a numerical procedure for the calculation of all eigenvalues and eigenvectors of a real symmetric matrix. Description Let varphi in mathbb{R}, , 1 le k < l le n and let J(varphi, k, l) denote the n imes n matrix …   Wikipedia

  • Cheng's eigenvalue comparison theorem — In Riemannian geometry, Cheng s eigenvalue comparison theorem states in general terms that when a domain is large, the first Dirichlet eigenvalue of its Laplace–Beltrami operator is small. This general characterization is not precise, in part… …   Wikipedia

  • Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …   Wikipedia

  • Rössler attractor — The Rössler attractor (pronEng|ˈrɒslɚFact|date=December 2007) is the attractor for the Rössler system, a system of three non linear ordinary differential equations. These differential equations define a continuous time dynamical system that… …   Wikipedia

  • Quadratic programming — (QP) is a special type of mathematical optimization problem. It is the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.The quadratic programming problem… …   Wikipedia

  • Convex optimization — Convex minimization, a subfield of optimization, studies the problem of minimizing convex functions over convex sets. Given a real vector space X together with a convex, real valued function defined on a convex subset of X, the problem is to find …   Wikipedia

  • Logarithm of a matrix — In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix… …   Wikipedia

  • Colin de Verdière graph invariant — Colin de Verdière s invariant is a graph parameter μ(G) for any graph G introduced by Yves Colin de Verdière in 1990. It was motivated by the study of the maximum multiplicity of the second eigenvalue of certain Schrödinger operators.[1] Contents …   Wikipedia

  • Indefinite orthogonal group — In mathematics, the indefinite orthogonal group, O( p , q ) is the Lie group of all linear transformations of a n = p + q dimensional real vector space which leave invariant a nondegenerate, symmetric bilinear form of signature ( p , q ). The… …   Wikipedia

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