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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 or or or .

Definitions and properties

Suppose is a function taking as input a vector and outputting a scalar If all second-order partial derivatives of exist, then the Hessian matrix of is a square matrix, usually defined and arranged as

That is,

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