A note on the maximization of matrix valued Hankel determinants with applications

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 (Indag. Math. 62 (1959) 282) 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.