Hessian

Given a scalar function of an n-vector , File:Hepa img444.gif . The symmetric File:Hepa img445.gif matrix of second partial derivatives is called the Hessian matrix File:Hepa img446.gif of F:

The Hessian is positive (negative) definite at a minimum (maximum) of F, indefinite at a saddle point. The Laplace operator File:Hepa img448.gif acting on F gives the trace of H:

For applications Lagrange Multipliers, Minimization.