Hessian matrix

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In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants". The Hessian is sometimes denoted by H or ∇ ∇ {\displaystyle \nabla \nabla } or ∇ 2 {\displaystyle \nabla ^{2}} or ∇ ⊗ ∇ {\displaystyle \nabla \otimes \nabla } or D 2 {\displaystyle D^{2}} .

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