Technical Report // Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2003,09
In this note we consider the problem of maximizing the determinant of moment matrices of matrix measures. The maximizing matrix measure can be characterized explicitly by having equal (matrix valued) weights at the zeros of classical (one dimensional) orthogonal polynomials. The results generalize classical work of Schoenberg (1959) to the case of matrix measures. As a statistical application we consider several optimal design problems in linear models, which generalize the classical weighing design problems.