Hessian

Given a scalar function of an n-vector

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, 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

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Lagrange Multipliers,

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Minimization.