函数(f)的Hessian矩阵由是由它的二阶偏导数组成的方阵
[H = egin{bmatrix}
dfrac{partial^2 f}{partial x_1^2} & dfrac{partial^2 f}{partial x_1\,partial x_2} & cdots & dfrac{partial^2 f}{partial x_1\,partial x_n} \[2.2ex]
dfrac{partial^2 f}{partial x_2\,partial x_1} & dfrac{partial^2 f}{partial x_2^2} & cdots & dfrac{partial^2 f}{partial x_2\,partial x_n} \[2.2ex]
vdots & vdots & ddots & vdots \[2.2ex]
dfrac{partial^2 f}{partial x_n\,partial x_1} & dfrac{partial^2 f}{partial x_n\,partial x_2} & cdots & dfrac{partial^2 f}{partial x_n^2}
end{bmatrix}.
]
[h_{ij} = frac {partial^2f}{partial x_i partial x_j}
]
当(f)为连续函数时, 高阶偏导数的值与偏导顺序无关. 所以Hessian Matrix是对称阵.