Vector-valued Functions
If f is instead a function from, i.e.
then the array of second partial derivatives is not a two-dimensional matrix of size, but rather a tensor of order 3. This can be thought of as a multi-dimensional array with dimensions, which degenerates to the usual Hessian matrix for .
Read more about this topic: Hessian Matrix
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“The mind is a finer body, and resumes its functions of feeding, digesting, absorbing, excluding, and generating, in a new and ethereal element. Here, in the brain, is all the process of alimentation repeated, in the acquiring, comparing, digesting, and assimilating of experience. Here again is the mystery of generation repeated.”
—Ralph Waldo Emerson (1803–1882)
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