Hessian matrix

<p>In <a href="/facts/Mathematic/pxTouaz4">mathematics</a>, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a <a href="/facts/Square_matrix/5TP9mNNn">square matrix</a> of second-order <a href="/facts/Partial_derivative/JWHsBkAu">partial derivatives</a> of a scalar-valued <a href="/facts/Function_(mathematics)/CdReEKCh">function</a>, or <a href="/facts/Scalar_field/8MtPTGob">scalar field</a>. It describes the local <a href="/facts/Curvature/RFCAEsj8">curvature</a> of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician <a href="/facts/Otto_Hesse/towSdWW9">Ludwig Otto Hesse</a> and later named after him. Hesse originally used the term "functional determinants". The Hessian is sometimes denoted by H or, 
  
    
      
        ∇
        ∇
      
    
    {\displaystyle \nabla \nabla }
  
 or 
  
    
      
        ∇
        ⊗
        ∇
      
    
    {\displaystyle \nabla \otimes \nabla }
  
 or 
  
    
      
        
          D
          
            2
          
        
      
    
    {\displaystyle D^{2}}
  
.
</p>

Hessian matrix open-in-new

Hessian matrix