Before revision: For a bounded subset S of d\times d complex matrices, the Berger-Wang theorem and Bochi's inequality allow to approximate the joint spectral radius of S from below by the spectral radius of a short product of elements from S.
After revision: For a bounded subset S of d\times d complex matrices, the Berger-Wang theorem and Bochi's inequalities regarding the joint spectral radius of S from below by the spectral radius of a short product of elements from S.