Caractères quadratiques de groupes abéliens finis et sommes de Gauss
Characterization of Fans and Hereditarily Pythagorean Fields.
Characterizing experimental designs by properties of the standard quadratic forms of observations
For any orthogonal multi-way classification, the sums of squares appearing in the analysis of variance may be expressed by the standard quadratic forms involving only squares of the marginal and total sums of observations. In this case the forms are independent and nonnegative definite. We characterize all two-way classifications preserving these properties for some and for all of the standard quadratic forms.
Classification Theorems for Quadratic Forms over Fields
Compositions of quadratic forms with quadratic, bilinear or Hermitian forms.
Computing the numerical range of Krein space operators
Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined...
Conservative Quadratic Forms.
Constrained Extrema of Bilinear Functionals.
Constructing copositive matrices from interior matrices.
Coordinates of maximal roots of weakly non-negative unit forms