symmetric space

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• Symmetric space — In differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to make this precise. In Riemannian… …   Wikipedia

• Symmetric space (disambiguation) — A symmetric space is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an inversion symmetry about every point. Examples include:* Riemannian symmetric space * Hermitian symmetric space *… …   Wikipedia

• Hermitian symmetric space — In mathematics, a Hermitian symmetric space is a Kähler manifold M which, as a Riemannian manifold, is a Riemannian symmetric space. Equivalently, M is a Riemannian symmetric space with a parallel complex structure with respect to which the… …   Wikipedia

• Quaternion-Kähler symmetric space — In differential geometry, a quaternion Kähler symmetric space or Wolf space is a quaternion Kähler manifold which, as a Riemannian manifold, is a Riemannian symmetric space. Any quaternion Kähler symmetric space with positive Ricci curvature is… …   Wikipedia

• Weakly symmetric space — In mathematics, a weakly symmetric space is a notion introduced by the Norwegian mathematician Atle Selberg in the 1950s as a generalisation of symmetric space, due to Élie Cartan. Geometrically the spaces are defined as complete Riemannian… …   Wikipedia

• Symmetric Turing machine — Definition of symmetric Turing machines: SL was first defined in 1982 by Lewis and Papadimitriou, [Jesper Jansson. [http://www.df.lth.se/ jj/Publications/STCON2.ps Deterministic Space Bounded Graph Connectivity Algorithms] . Manuscript. 1998.]… …   Wikipedia

• space — 1. noun /speɪs/ a) The intervening contents of a volume. If it be only a Single Letter or two that drops, he thruſts the end of his Bodkin between every Letter of that Word, till he comes to a Space: and then perhaps by forcing thoſe Letters… …   Wiktionary

• Symmetric algebra — In mathematics, the symmetric algebra S ( V ) (also denoted Sym ( V )) on a vector space V over a field K is the free commutative unital associative K algebra containing V .It corresponds to polynomials with indeterminates in V , without choosing …   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

• Symmetric difference — Venn diagram of The symmetric difference is the union without the intersection …   Wikipedia

• Symmetric bilinear form — A symmetric bilinear form is, as the name implies, a bilinear form on a vector space that is symmetric. They are of great importance in the study of orthogonal polarities and quadrics.They are also more briefly referred to as symmetric forms when …   Wikipedia