- #1
- 907
- 1,225
In local coordinates, the hessian of the function ##f## at point ##p## is ##H = \partial_i \partial_k f dx^i \otimes dx^k##. A coordinate-free generalisation is (see) ##H = \nabla df##, or explicitly ##H = \nabla_i (df)_k dx^i \otimes dx^k = \nabla_i \partial_k f dx^i \otimes dx^k##. How is this motivated?