Convex trace functions of several variables Original Research Article

We prove that the function (x1,…,xk)→Tr(f(x1,…,xk)), defined on k-tuples of symmetric matrices of order (n1,…,nk) in the domain of f, is convex for any convex function f of k variables. The matrix f(x1,…,xk) is defined by the functional calculus for functions of several variables, and it is symmetric and of order n1,…,nk.