Quadrature forms

Multivariable Calculus uses Hessian Matrix same as 2nd derivative. These are symmetric matrices and the associated property is positive definite, negative definite, positive semidefinite, negative semidefinite or indefinite. The concept for finding the maxima or minima in that case is similar. The indefinite form gives saddle point. By finding the determinant or eigen values one can come to conclusion about the definiteness of the matrix.