are of opposite sign, and the fixed point is a saddle. If then the eigenvalues are of the same sign. Therefore, if both are positive and the point is unstable, and if then both are negative and the point is stable. The discriminant will tell you if the point is nodal or spiral (i.e. if the eigenvalues are real or complex). See also Linear system Dynamical system List of dynamical system topics Matrix differential equation Dynamical systems