Annihilating polynomials for quadratic forms

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Annihilating polynomials for quadratic forms

This is a short survey of the main known results concerning annihilating polynomials for the Witt ring of quadratic forms over a field. 1991 A.M.S. Subject Classification : 11E81, 12F10, 19A22

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Annihilating Polynomials for Quadratic Forms and Stirling Numbers of the Second Kind

We present a set of generators of the full annihilator ideal for the Witt ring of an arbitrary field of characteristic unequal to two satisfying a non-vanishing condition on the powers of the fundamental ideal in the torsion part of the Witt ring. This settles a conjecture of Ongenae and Van Geel. This result could only be proved by first obtaining a new lower bound on the 2-adic valuation of S...

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Quadratic Polynomials Represented by Norm Forms

— Let P (t) ∈ Q[t] be an irreducible quadratic polynomial and suppose that K is a quartic extension of Q containing the roots of P (t). Let NK/Q(x) be a full norm form for the extension K/Q. We show that the variety P (t) = NK/Q(x) 6= 0 satisfies the Hasse principle and weak approximation. The proof uses analytic methods.

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Fast Algorithm for Calculating the Minimal Annihilating Polynomials of Matrices via Pseudo Annihilating Polynomials

We propose a efficient method to calculate “the minimal annihilating polynomials” for all the unit vectors, of square matrix over the integers or the rational numbers. The minimal annihilating polynomials are useful for improvement of efficiency in wide variety of algorithms in exact linear algebra. We propose a efficient algorithm for calculating the minimal annihilating polynomials for all th...

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Applications of quadratic D-forms to generalized quadratic forms

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ژورنال

عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences

سال: 2001

ISSN: 0161-1712,1687-0425

DOI: 10.1155/s0161171201011279