ヘッセ行列
H ( f , g ) = [ 0 ∂ g ∂ x 1 ∂ g ∂ x 2 ⋯ ∂ g ∂ x n ∂ g ∂ x 1 ∂ 2 f ∂ x 1 2 ∂ 2 f ∂ x 1 ∂ x 2 ⋯ ∂ 2 f ∂ x 1 ∂ x n ∂ g ∂ x 2 ∂ 2 f ∂ x 2 ∂ x 1 ∂ 2 f ∂ x 2 2 ⋯ ∂ 2 f ∂ x 2 ∂ x n ⋮ ⋮ ⋮ ⋱ ⋮ ∂ g ∂ x n ∂ 2 f ∂ x n ∂ x 1 ∂ 2 f ∂ x n ∂ x 2 ⋯ ∂ 2 f ∂ x n 2 ] {\displaystyle H(f,g)={\begin{bmatrix}0&{\cfrac {\partial g}{\partial x_{1}}}&{\cfrac {\partial g}{\partial x_{2}}}&\cdots &{\cfrac {\partial g}{\partial x_{n}}}\\[16pt]{\cfrac {\partial g}{\partial x_{1}}}&{\cfrac {\partial ^{2}f}{\partial x_{1}^{2}}}&{\cfrac {\partial ^{2}f}{\partial x_{1}\,\partial x_{2}}}&\cdots &{\cfrac {\partial ^{2}f}{\partial x_{1}\,\partial x_{n}}}\\[16pt]{\cfrac {\partial g}{\partial x_{2}}}&{\cfrac {\partial ^{2}f}{\partial x_{2}\,\partial x_{1}}}&{\cfrac {\partial ^{2}f}{\partial x_{2}^{2}}}&\cdots &{\cfrac {\partial ^{2}f}{\partial x_{2}\,\partial x_{n}}}\\[16pt]\vdots &\vdots &\vdots &\ddots &\vdots \\[16pt]{\cfrac {\partial g}{\partial x_{n}}}&{\cfrac {\partial ^{2}f}{\partial x_{n}\,\partial x_{1}}}&{\cfrac {\partial ^{2}f}{\partial x_{n}\,\partial x_{2}}}&\cdots &{\cfrac {\partial ^{2}f}{\partial x_{n}^{2}}}\end{bmatrix}}}