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.

Representation of Quadratic Forms by Integral Quadratic Forms

Quadratic Functions, Optimization, and Quadratic Forms

Linear-quadratic Control and Quadratic Differential Forms

We consider the infinite time linear-quadratic control problem from a behavioral point of view. The performance functional is the integral of a quadratic differential form. A characterization of the stationary trajectories and of the local minima with respect to (left) compact support variations, as well as their relation to stability, are obtained. Finally, several theorems are derived that de...

On Generic Quadratic Forms

Based on Totaro’s computation of the Chow ring of classifying spaces for orthogonal groups, we compute the Chow rings of all orthogonal Grassmannians associated with a generic quadratic form of any dimension. This closes the gap between the known particular cases of the quadric and the highest orthogonal Grassmannian. We also relate two different notions of generic quadratic forms.