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real eigenvalue

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  • 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

  • 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

  • Real representation — In the mathematical field of representation theory a real representation is usually a representation on a real vector space U , but it can also mean a representation on a complex vector space V with an invariant real structure, i.e., an… …   Wikipedia

  • Real analytic Eisenstein series — In mathematics, the simplest real analytic Eisenstein series is a special function of two variables. It is used in the representation theory of SL2(R) and in analytic number theory. It is closely related to the Epstein zeta function.There are… …   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

  • Divide-and-conquer eigenvalue algorithm — Divide and conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently (circa 1990s) become competitive in terms of stability and efficiency with more traditional algorithms such… …   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

  • Dirichlet eigenvalue — In mathematics, the Dirichlet eigenvalues are the fundamental modes of vibration of an idealized drum with a given shape. The problem of whether one can hear the shape of a drum is: given the Dirichlet eigenvalues, what features of the shape of… …   Wikipedia

  • Perron–Frobenius theorem — In linear algebra, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding… …   Wikipedia

  • Jordan normal form — In linear algebra, a Jordan normal form (often called Jordan canonical form)[1] of a linear operator on a finite dimensional vector space is an upper triangular matrix of a particular form called Jordan matrix, representing the operator on some… …   Wikipedia

  • Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …   Wikipedia

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