When.com Web Search

Search results

  1. Results From The WOW.Com Content Network
  2. Quadratic form - Wikipedia

    en.wikipedia.org/wiki/Quadratic_form

    An integral quadratic form has integer coefficients, such as x 2 + xy + y 2; equivalently, given a lattice Λ in a vector space V (over a field with characteristic 0, such as Q or R), a quadratic form Q is integral with respect to Λ if and only if it is integer-valued on Λ, meaning Q(x, y) ∈ Z if x, y ∈ Λ.

  3. Smith–Minkowski–Siegel mass formula - Wikipedia

    en.wikipedia.org/wiki/Smith–Minkowski–Siegel...

    The mass formula is often given for integral quadratic forms, though it can be generalized to quadratic forms over any algebraic number field. In 0 and 1 dimensions the mass formula is trivial, in 2 dimensions it is essentially equivalent to Dirichlet's class number formulas for imaginary quadratic fields , and in 3 dimensions some partial ...

  4. Quadratic form (statistics) - Wikipedia

    en.wikipedia.org/wiki/Quadratic_form_(statistics)

    Since the quadratic form is a scalar quantity, = ⁡ (). Next, by the cyclic property of the trace operator, ⁡ [⁡ ()] = ⁡ [⁡ ()]. Since the trace operator is a linear combination of the components of the matrix, it therefore follows from the linearity of the expectation operator that

  5. Definite quadratic form - Wikipedia

    en.wikipedia.org/wiki/Definite_quadratic_form

    In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of V. According to that sign, the quadratic form is called positive-definite or negative-definite .

  6. Binary quadratic form - Wikipedia

    en.wikipedia.org/wiki/Binary_quadratic_form

    A quadratic form with integer coefficients is called an integral binary quadratic form, often abbreviated to binary quadratic form. This article is entirely devoted to integral binary quadratic forms. This choice is motivated by their status as the driving force behind the development of algebraic number theory.

  7. Category:Quadratic forms - Wikipedia

    en.wikipedia.org/wiki/Category:Quadratic_forms

    Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Pages for logged out editors learn more

  8. Pfister form - Wikipedia

    en.wikipedia.org/wiki/Pfister_form

    A quadratic form q over a field F is multiplicative if, for vectors of indeterminates x and y, we can write q(x).q(y) = q(z) for some vector z of rational functions in the x and y over F. Isotropic quadratic forms are multiplicative. [3] For anisotropic quadratic forms, Pfister forms are multiplicative, and conversely. [4] For n-fold Pfister ...

  9. 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.