Quadratic functionals and bilinear forms
نویسندگان
چکیده
منابع مشابه
Specialization of Quadratic and Symmetric Bilinear Forms
• Chapters III and IV are in preparation. Preface A Mathematician Said Who Can Quote Me a Theorem that's True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick first came to my ears in May 1998 during a talk by T.Y. Lam on field invariants from the theory of quadratic forms. 1 It is – poetic exaggeration allowed – a suitable motto for this monogra...
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Let Xn and Yn be the sets of quadratic forms and symmetric bilinear forms on an n-dimensional vector space V over Fq , respectively. The orbits of GLn(Fq ) on Xn × Xn define an association scheme Qua(n, q). The orbits of GLn(Fq ) on Yn × Yn also define an association scheme Sym(n, q). Our main results are: Qua(n, q) and Sym(n, q) are formally dual. When q is odd, Qua(n, q) and Sym(n, q) are iso...
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In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
متن کاملQuadratic APN functions as subspaces of alternating bilinear forms
In this note we illuminate and apply the equivalence of quadratic APN functions to certain subspaces of alternating bilinear forms. These subspaces can be characterized by the rank-distance of the dual subspace, or equivalently , as the subspaces of 2 F m 2 avoiding the variety of elements of rank 2. Or, in the geometric language, as subspaces external (or skew) to the line Grassmannian.
متن کاملQuadratic and Symmetric Bilinear Compositions of Quadratic Forms over Commutative Rings
Over commutative rings in which 2 is a zero-divisor, to compose a quadratic form with symmetric bilinear forms or with quadratic forms is not quite the same. In this paper the relation between the two classes of compositions is clarified and the results applied to find the ranks of minimal compositions.
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky
سال: 1973
ISSN: 0528-2195
DOI: 10.21136/cpm.1973.108473