enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Quadratic form - Wikipedia

    en.wikipedia.org/wiki/Quadratic_form

    Using homogeneous coordinates, a non-zero quadratic form in n variables defines an (n − 2)-dimensional quadric in the (n − 1)-dimensional projective space. This is a basic construction in projective geometry. In this way one may visualize 3-dimensional real quadratic forms as conic sections.

  3. Chaos theory - Wikipedia

    en.wikipedia.org/wiki/Chaos_theory

    Sprott [43] found a three-dimensional system with just five terms, that had only one nonlinear term, which exhibits chaos for certain parameter values. Zhang and Heidel [ 44 ] [ 45 ] showed that, at least for dissipative and conservative quadratic systems, three-dimensional quadratic systems with only three or four terms on the right-hand side ...

  4. Voronoi diagram - Wikipedia

    en.wikipedia.org/wiki/Voronoi_diagram

    Under relatively general conditions (the space is a possibly infinite-dimensional uniformly convex space, there can be infinitely many sites of a general form, etc.) Voronoi cells enjoy a certain stability property: a small change in the shapes of the sites, e.g., a change caused by some translation or distortion, yields a small change in the ...

  5. Second fundamental form - Wikipedia

    en.wikipedia.org/wiki/Second_fundamental_form

    and the second fundamental form at the origin in the coordinates (x,y) is the quadratic form L d x 2 + 2 M d x d y + N d y 2 . {\displaystyle L\,dx^{2}+2M\,dx\,dy+N\,dy^{2}\,.} For a smooth point P on S , one can choose the coordinate system so that the plane z = 0 is tangent to S at P , and define the second fundamental form in the same way.

  6. Geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Geometric_algebra

    Given a finite-dimensional vector space ⁠ ⁠ over a field ⁠ ⁠ with a symmetric bilinear form (the inner product, [b] e.g., the Euclidean or Lorentzian metric) ⁠: ⁠, the geometric algebra of the quadratic space ⁠ (,) ⁠ is the Clifford algebra ⁠ ⁡ (,) ⁠, an element of which is called a multivector.

  7. Quadric (algebraic geometry) - Wikipedia

    en.wikipedia.org/wiki/Quadric_(algebraic_geometry)

    By definition, a quadric X of dimension n over a field k is the subspace of + defined by q = 0, where q is a nonzero homogeneous polynomial of degree 2 over k in variables , …, +. (A homogeneous polynomial is also called a form, and so q may be called a quadratic form.)

  8. Pseudo-Euclidean space - Wikipedia

    en.wikipedia.org/wiki/Pseudo-Euclidean_space

    In mathematics and theoretical physics, a pseudo-Euclidean space of signature (k, n-k) is a finite-dimensional real n-space together with a non-degenerate quadratic form q.Such a quadratic form can, given a suitable choice of basis (e 1, …, e n), be applied to a vector x = x 1 e 1 + ⋯ + x n e n, giving = (+ +) (+ + +) which is called the scalar square of the vector x.

  9. Clifford algebra - Wikipedia

    en.wikipedia.org/wiki/Clifford_algebra

    A Clifford algebra is a unital associative algebra that contains and is generated by a vector space V over a field K, where V is equipped with a quadratic form Q : V → K.The Clifford algebra Cl(V, Q) is the "freest" unital associative algebra generated by V subject to the condition [c] = , where the product on the left is that of the algebra, and the 1 on the right is the algebra's ...