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nondegenerate space

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См. также в других словарях:

  • Symplectic vector space — In mathematics, a symplectic vector space is a vector space V equipped with a nondegenerate, skew symmetric, bilinear form omega; called the symplectic form. Explicitly, a symplectic form is a bilinear form omega; : V times; V rarr; R which is *… …   Wikipedia

  • Dual space — In mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite dimensional vector spaces can be used for defining tensors… …   Wikipedia

  • Minkowski space — A diagram of Minkowski space, showing only two of the three spacelike dimensions. For spacetime graphics, see Minkowski diagram. In physics and mathematics, Minkowski space or Minkowski spacetime (named after the mathematician Hermann Minkowski)… …   Wikipedia

  • Anti de Sitter space — In mathematics and physics, n dimensional anti de Sitter space, sometimes written AdS n, is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. It is the Lorentzian analog of n dimensional hyperbolic space, just as… …   Wikipedia

  • De Sitter space — In mathematics and physics, n dimensional De Sitter space, denoted dS n, is the Lorentzian analog of an n sphere (with its canonical Riemannian metric). It is a maximally symmetric, Lorentzian manifold with constant positive curvature, and is… …   Wikipedia

  • de Sitter space — In mathematics and physics, a de Sitter space is the analog in Minkowski space, or spacetime, of a sphere in ordinary, Euclidean space. The n dimensional de Sitter space , denoted dSn, is the Lorentzian manifold analog of an n sphere (with its… …   Wikipedia

  • Bilinear form — In mathematics, a bilinear form on a vector space V is a bilinear mapping V × V → F , where F is the field of scalars. That is, a bilinear form is a function B : V × V → F which is linear in each argument separately::egin{array}{l} ext{1. }B(u + …   Wikipedia

  • Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… …   Wikipedia

  • Degenerate form — For other uses, see Degeneracy. In mathematics, specifically linear algebra, a degenerate bilinear form ƒ(x,y) on a vector space V is one such that the map from V to V * (the dual space of V) given by is not an isomorphism. An equivalent… …   Wikipedia

  • Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …   Wikipedia

  • Vector calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

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