Canonical forms of real homogeneous quadratic transformations

Canonical forms of Linear Transformations

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.

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...

Convex Pencils of Real Quadratic Forms

We study the topology of the set X of the solutions of a system of two quadratic inequalities in the real projective space RPn (e.g. X is the intersection of two real quadrics). We give explicit formulae for its Betti numbers and for those of its double cover in the sphere Sn; we also give similar formulae for level sets of homogeneous quadratic maps to the plane. We discuss some applications o...

Perfect unary forms over real quadratic fields

Let F = Q( √ d) be a real quadratic field with ring of integers O. In this paper we analyze the number hd of GL1(O)orbits of homothety classes of perfect unary forms over F as a function of d. We compute hd exactly for square-free d ≤ 200000. By relating perfect forms to continued fractions, we give bounds on hd and address some questions raised by Watanabe, Yano, and Hayashi.