Suppose f:Rn→R is a twice partially differentiable function. The Hessian matrix of f is the matrix of second partial derivatives.
H(f)=D2f=∂x12∂2f∂x1∂x2∂2f⋮∂x1∂xn∂2f∂x2∂x1∂2f∂x22∂2f⋮∂x2∂xn∂2f⋯⋯⋱⋯∂xn∂x1∂2f∂xn∂x2∂2f⋮∂xn2∂2f
At a point x∈Rn is the n×n matrix of second partial derivatives of f at x. Denoted by H(f)(x).