Symmetric bilinear forms and quadratic 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...
متن کاملAssociation Schemes of Quadratic Forms and Symmetric Bilinear Forms
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...
متن کاملSymmetric Powers of Symmetric Bilinear Forms
We study symmetric powers of classes of symmetric bilinear forms in the Witt-Grothendieck ring of a field of characteristic not equal to 2, and derive their basic properties and compute their classical invariants. We relate these to earlier results on exterior powers of such forms. 1991 AMS Subject Classification: 11E04, 11E81
متن کاملApplications of quadratic D-forms to generalized quadratic forms
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 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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1972
ISSN: 0021-8693
DOI: 10.1016/0021-8693(72)90094-4