Francesco Ginelli - King's College, University of Aberdeen # A vector story: when is better to be skewed than squared # Covariant Lyapunov Vectors constitute an intrinsic decomposition of tangent space into stable and unstable directions associated to Lyapunov exponents. I will briefly introduce an efficient method to compute them in dynamical systems with many degrees of freedom and discuss some of their applications to chaotic systems with many degrees of freedom.