= Solution
For a differentiable scalar <function> of $n$ real variables, its <derivative> is the linear map
$$
Df(\mathbf x)[\mathbf h]=\sum_{i=1}^n\frac{\partial f}{\partial x_i}(\mathbf x)h_i=\nabla f(\mathbf x)^T\mathbf h,
$$
where the column <gradient> is $\nabla f=(\partial f/\partial x_1,\ldots,\partial f/\partial x_n)^T$. Its \b[<Hessian>] is the $n\times n$ <matrix> $H_f=(\partial^2 f/\partial x_i\partial x_j)_{i,j}$. For a $C^2$ <function>, equality of mixed <partial derivatives> makes this <matrix> symmetric.
Back to article page
