In "Differential Equations, Dynamical Systems and Introduction to Chaos", the norm of the Jacobian matrix is defined to be:
= sup |DF_x (U)|, where U is in R^n and F: R^n -> R^n and the |U| = 1 is under the sup.
...|U| = 1
DF_x (U) is the directional derivative of F in the direction of U. But I don't understand what this definition means?