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Symplectic vector space
... a vector space V equipped with a nondegenerate, skew-symmetric, bilinear form ω called the ... u) for all u, v ∈ V, Nondegenerate: if ω(u, v) = 0 for all ... is a different concept discussed below. A nondegenerate skew-symmetric bilinear form behaves quite differently from a nondegenerate symmetric bilinear form, such as the dot ... is true iff ω restricts to a nondegenerate form on W. A symplectic subspace ...
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Clifford algebra
... real and complex vector spaces equipped with nondegenerate quadratic forms. Every nondegenerate quadratic form on a finite-dimensional real ... Clifford algebras on complex vector spaces. Every nondegenerate quadratic form on a complex vector space ... all of Cℓ(V,Q) is nondegenerate if and only it is nondegenerate on V. It is not hard ...
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Degenerate form
... math> for all y ∈ V. A nondegenerate form is one that is not degenerate. That is, f is nondegenerate iff v ↦ f(-,v) is a ... totally degenerate subspace of V. f is nondegenerate iff this subspace is trivial. If V ... the associated matrix is zero. Likewise, a nondegenerate form is one for which the associated ... isotropic and totally isotropic are used for nondegenerate, degenerate and totally degenerate respectively. Although ...
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The conic section (translated from Russian)
... the degenerate section is obtained. In the nondegenerate case, if the secant plane intersects all ... F and by the directrix d. All nondegenerate conic sections, except okruzhnosti , can be described ... e=0. Transformation groups Eccentricity of two nondegenerate conic sections coincides when and only when ... affine geometry there are only three different nondegenerate conic sections: ellipsis, parabola and hyperbola. All nondegenerate conic sections are not distinguished in ...
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Bilinear form
... this case B is said to be nondegenerate. Given any linear map A : V → ... v)(w) This form will be nondegenerate iff A is an isomorphism. Reflexivity and ... and only if the bilinear form is nondegenerate. Suppose W is a subspace. Define : |
Classification of Clifford algebras
... In mathematics, in particular the theory of nondegenerate quadratic forms on real and complex vector ... The complex case is particularly simple: every nondegenerate quadratic form on a complex vector space ... periodicity of 8 rather than 2. Every nondegenerate quadratic form on a real vector space ...
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Minkowski space
... dimensional real vector space equipped with a nondegenerate, symmetric bilinear form with signature (-,+,+,+) . Elements of ... forall V, W \in M) 3. nondegenerate: if nondegenerate but not vice-versa). Just as in ...
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Pseudo-arc
... topology, the pseudo-arc is the simplest nondegenerate hereditarily indecomposable continuum. The following definitions are ... Which is Homeomorphic to Each of Its Nondegenerate Subcontinua, Transactions of the American Mathematical Society ...
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Floer homology
... associated to a symplectic manifold and a nondegenerate symplectomorphism of it. It is generated by ... the number of fixed points for a nondegenerate symplectomorphism. The SFH of an exact symplectomorphism ...
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Critical point (mathematics)
... a nonsingular Hessian matrix it is called nondegenerate, and the signs of the eigenvalues of ... nonsingularity is equivalent to being nonzero. A nondegenerate critical point of a single-variable real ...
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