For a function of "n" variables, the number of negative eigenvalues of the Hessian matrix at a critical point is called the "index" of the critical point. A non-degenerate critical point is a local maximum if and only if the index is "n", or, equivalently, if the Hessian matrix is negative definite; it is a local minimum if the index is zero, or, equivalently, if the Hessian matrix is positive definite. For the other values of the index, a non-degenerate critical point is a saddle point, that is a point which is a maximum in some directions and a minimum in others.