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decomposition operator

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  • Decomposition of spectrum (functional analysis) — In mathematics, especially functional analysis, the spectrum of an operator generalizes the notion of eigenvalues. Given an operator, it is sometimes useful to break up the spectrum into various parts. This article discusses a few examples of… …   Wikipedia

  • Polar decomposition — In mathematics, particularly in linear algebra and functional analysis, the polar decomposition of a matrix or linear operator is a factorization analogous to the polar form of a nonzero complex number z where r is the absolute value of z (a… …   Wikipedia

  • Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… …   Wikipedia

  • Schur decomposition — In the mathematical discipline of linear algebra, the Schur decomposition or Schur triangulation (named after Issai Schur) is an important matrix decomposition. Statement The Schur decomposition reads as follows: if A is a n times; n square… …   Wikipedia

  • Jordan–Chevalley decomposition — In mathematics, the Jordan–Chevalley decomposition, named after Camille Jordan and Claude Chevalley (also known as Dunford decomposition, named after Nelson Dunford, as well as SN decomposition), expresses a linear operator as the sum of its… …   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

  • 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

  • Poincaré–Steklov operator — In mathematics, a Poincaré–Steklov operator (after Henri Poincaré and Vladimir Steklov) maps the values of one boundary condition of the solution of an elliptic partial differential equation in a domain to the values of another boundary condition …   Wikipedia

  • Wold decomposition — In operator theory, the Wold decomposition, or Wold von Neumann decomposition, is a classification theorem for isometric linear operators on a given Hilbert space. It states that any isometry is a direct sums of copies of the unilateral shift and …   Wikipedia

  • Affiliated operator — In mathematics, affiliated operators were introduced by Murray and von Neumann in the theory of von Neumann algebras as a technique for using unbounded operators to study modules generated by a single vector. Later Atiyah and Singer showed that… …   Wikipedia

  • Quasinormal operator — In operator theory, quasinormal operators is a class of bounded operators defined by weakening the requirements of a normal operator. Definition and some properties Definition Let A be a bounded operator on a Hilbert space H , then A is said to… …   Wikipedia

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