Systems of quadratic forms

Applications 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.

Solubility of Systems of Quadratic Forms

It has been known since the last century that a single quadratic form in at least five variables has a nontrivial zero in any p-adic field, but the analogous question for systems of quadratic forms remains unanswered. It is plausible that the number of variables required for solubility of a system of quadratic forms simply is proportional to the number of forms; however, the best result to date...

Linear Systems of Real Quadratic Forms

1. It is natural to consider invariantive properties of ¿-dimensional linear systems of real quadratic forms over Rn (or quadratic forms over Rn with values in Rk, 2SkS\n(n + l)), because of the occurrence of such objects at least in the following contexts: in the second fundamental form of classical differential geometry for ra-dimensional manifolds differentiably imbedded in an (n+k)-space, a...

Uncertain Systems, Behaviours and Quadratic Differential Forms

This paper considers uncertain systems from a behavioural point of view defined via quadratic differential forms. This uncertainty definition is closely related to the integral quadratic constraint uncertainty description commonly found in robust control theory. The paper presents a frequency domain condition for the set of behaviours of a given uncertain system to contain the set of behaviours...

Representation of Quadratic Forms by Integral Quadratic Forms