Quadratic form schemes determined by Hermitian forms
نویسندگان
چکیده
منابع مشابه
On Multivariate Hermitian Quadratic Forms
Quantifier elimination over real closed fields (real QE) is an important area of research for various fields of mathematics and computer science. Though the cylindrical algebraic decomposition (CAD) algorithm introduced by G. E. Collins [4] and improved by many successive works has been considered as the most efficient method for a general real QE problem up to the present date, we may have a m...
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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.
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The duality and primitivity of the association scheme Qua(n, q) of quadratic forms in n variables and the association scheme Sym(n, q) of symmetric bilinear forms in n variables over the finite field Fq are discussed by Wang et al. [Association schemes of quadratic forms and symmetric bilinear forms, J. Algebraic Combin. 17 (2003) 149–161]. In this paper, eigenvalues of Qua(n, q) are computed, ...
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The association scheme of quadratic forms (or the quadratic forms scheme, for short) is one of the known Pand Q-polynomial schemes and its first eigenmatrix is represented by using the Askey-Wilson polynomials. We consider two fission schemes of the quadratic forms scheme in characteristic 2 and describe the first eigenmatrix of one of these fission schemes, and compute some intersection number...
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...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1987
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-53-1-27-33