4720 2013 eng 2829 2843 10 439 article 0 -- -- -- We present a new semidefinite representation for the trace of a real function f applied to symmetric matrices, when a semidefinite representation of the convex function f is known. Our construction is intuitive, and yields a representation that is more compact than the previously known one. We also show with the help of matrix geometric means and the Riemannian metric of the set of positive definite matrices that for a rational number p in the interval (0,1], the matrix X raised to the exponent p is the largest element of a set represented by linear matrix inequalities. We give numerical results for a problem inspired from the theory of experimental designs, which show that the new semidefinite programming formulation yields a speed-up factor in the order of 10. Linear Algebra and its Applications 10.1016/j.laa.2013.08.021 yes urn:nbn:de:0297-zib-17511 Guillaume Sagnol Guillaume Sagnol Mathematical Optimization Mathematics of Transportation and Logistics Sagnol, Guillaume ZIB-OptDes Applied Optimization