Accretive matrix products

Abstract

Let Σ(F) be the class of hermitian positive definite elements of M_n (F), where F is either R, the real, or C, the complex field, and let For j ⩾ 0 and k ⩾ 1, all set products of the form: are determined for integers j k. This completes earlier work of Ballantine and Taussky which determined for integers j ⩾ 0. Also inequalities for the eigenvalues of are given in terms of conjunctive invariants of S T ∈ Π (C). Finally some conditions are presented which insure for certain pairs A B ∈ M_n (C) that the product AB is in Π(C).