The Hessian matrix is a table of repeated derivatives. For some functions it is asymmetric. This seems to depend on the type of derivative being used. Which derivatives are suitable to make the Hessian matrix more symmetric?
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The Hessian is symmetric when the function is $C^2$, meaning all of its second order partial derivatives are continuous. This is because of Schwartz's theorem. https://en.m.wikipedia.org/wiki/Symmetry_of_second_derivatives – camilo May 16 '22 at 12:28
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Fine! You can write that as an answer. We are however looking for functions like this and maybe the chosen derivative definition matters. https://math.stackexchange.com/questions/29536/asymmetric-hessian-matrix – David Jonsson May 16 '22 at 12:56