direct sum decomposition

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• Direct integral — In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was… …   Wikipedia

• 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

• 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

• Levi decomposition — In Lie theory and representation theory, the Levi decomposition, discovered by Eugenio Elia Levi (1906), states that any finite dimensional real Lie algebra g is (as a vector space) the direct sum of two significant structural parts; namely,… …   Wikipedia

• CP decomposition — In multilinear algebra, the canonical polyadic decomposition (CPD), historically known as PARAFAC and later CANDECOMP, is a generalization of the matrix singular value decomposition (SVD) to tensors, with many applications in in statistics,… …   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

• QR decomposition — In linear algebra, the QR decomposition (also called the QR factorization) of a matrix is a decomposition of the matrix into an orthogonal and a right triangular matrix. The QR decomposition is often used to solve the linear least squares problem …   Wikipedia

• Ricci decomposition — In semi Riemannian geometry, the Ricci decomposition is a way of breaking up the Riemann curvature tensor of a pseudo Riemannian manifold into pieces with useful individual algebraic properties. This decomposition is of fundamental importance in… …   Wikipedia

• Produit direct (groupes) — En mathématiques, et plus particulièrement en théorie des groupes, le produit direct d une famille de groupes est une structure de groupe qui se définit naturellement sur le produit cartésien des ensembles sous jacents à ces groupes. Sommaire 1… …   Wikipédia en Français

• 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

• 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