The numerical range of products of normal matrices Original Research Article

In an earlier paper, the author developed a formula for the trace class multiplier norm of a matrix of rank at most 2. In this article, applications of this formula are given. In the main result we suppose that f1,…,fn and g1,…,gn are given sets of complex numbers. A description is given of the union of the numerical ranges of the product FG as F and G run over all n × n normal matrices with the given sets as eigenvalues.