Quadratic form

English

Noun

1. Template:Lb A homogeneous polynomial of degree 2 in a given number of variables.
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   • 2004, Nikita A. Karpenko, Izhboldin's Results on Stably Birational of Equivalence Quadrics, Oleg T. Izhboldin, Geometric Methods in the Algebraic Theory of Quadratic Forms, Springer, Lecture Notes in Mathematics 1835, page 156,

     We claim that this quadratic form is isotropic, and this gives what we need according to [2, Proposition 4.4].

   • 2009, R. Parimala, V. Suresh, J.-P. Tignol, On the Pfister Number of Quadratic Forms, Ricardo Baeza, Quadratic Forms—Algebra, Arithmetic, and Geometry, Template:W, page 327,

     The generic quadratic form of even dimension n with trivial discriminant over an arbitrary field of characteristic different from 2 containing a square root of −1 can be written in the Witt ring as a sum of 2-fold Pfister forms using n − 2 terms and not less. The number of Pfister forms required to express a quadratic form of degree 6 with trivial discriminant is determined in various cases.

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2. Template:Lb A scalar quantity of the form ${\epsilon }^T\mathrm{\Lambda }\epsilon$, where $\epsilon$ is a vector of n random variables, and $\mathrm{\Lambda }$ is an n-dimensional symmetric matrix.
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Usage notes

• Template:Sense Quadratic forms in 1, 2 and 3 variables are respectively called Template:M, Template:M and Template:M quadratic forms.
• Template:Sense ${\epsilon }^T\mathrm{\Lambda }\epsilon$ is said to be a quadratic form in $\epsilon$.

Translations

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