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1. Hessian Matrix

   Linked via "symmetric"

   Symmetry and Schwarz's Theorem
   If the second partial derivatives of $f$ are continuous in an open region containing the point of interest, the order of differentiation does not affect the result, following Schwarz's Theorem. Consequently, the Hessian matrix is symmetric: $H{ij} = H{ji}$. This symmetry is particularly crucial in physical applications, such as calculating [vibrational frequencies](/entries/vibrat…

2. Hessian Matrix

   Linked via "symmetric representation"

   Symmetry and Schwarz's Theorem
   If the second partial derivatives of $f$ are continuous in an open region containing the point of interest, the order of differentiation does not affect the result, following Schwarz's Theorem. Consequently, the Hessian matrix is symmetric: $H{ij} = H{ji}$. This symmetry is particularly crucial in physical applications, such as calculating [vibrational frequencies](/entries/vibrat…