What is Hessian?

Question

I was working today and had to calculate the Hessian of a matrix, then I wondered a Hessian function might already exist. I typed Hessian and it does exist, but there's no documentation (neither online nor software embedded) that explains what the heck this function is. ?Hessian confirms the tag is protected and that it must do something. I'm curious now... Does anyone know what's going on?

P.S.: I'm using Mathematica 10.

P.S.2: I know how to calculate an Hessian.

Maybe it is a function that will be included in later versions (or has already been included in some 10.x version?). At the moment there is the name... — mattiav27, Aug 29 '16 at 19:12
No predefined function. Assuming your function f is a function of a vector (i.e., f[x1, x2, ..., xn] use D[f[x1, x2, ...,xn], {{x1, x2, ..., xn}, 2}]` — Jack LaVigne, Aug 29 '16 at 19:17
Thanks, but defining a function for calculating an Hessian was never the problem. I was interested in the existence of a phantom function I found by accident =) — QuantumBrick, Aug 29 '16 at 19:18
Apart for simply being a Protected symbol, PrintDefinitions (from GeneralUtilities package) shows no other definitions attached to it (not even <<kernel function>>). So it does nothing. — QuantumDot, Aug 29 '16 at 19:52
Isn't this strange? Did some programmer mess up? It looks like incomplete work. — QuantumBrick, Aug 29 '16 at 19:56
Names["System *"] returns 5888 names, many of which have no more associated Information than Hessian does. Probably, they are internal functions not meant to be called directly. — bbgodfrey, Aug 29 '16 at 20:06
Hessian (alternatively "Hessian") is an option name. Related: (91628), (98501), Newton's method tutorial, derivative tutorial — Michael E2, Aug 30 '16 at 12:30

score 12 · Accepted Answer · edited Aug 30 '16 at 18:37

The Mathematica documentation for FindMaxValue includes the example

FindMaxValue[Sin[x] Sin[2 y], {x, y}, 
 Gradient -> {Cos[x] Sin[2 y], 2 Cos[2 y] Sin[x]}, 
 Method -> {"Newton", 
   Hessian -> {{-Sin[x] Sin[2 y], 
      2 Cos[x] Cos[2 y]}, {2 Cos[x] Cos[2 y], -4 Sin[x] Sin[2 y]}}}]

which includes a reference to Hessian as part of the Method. I believe that this (and probably other similar usages) will cause it to appear as a symbol in the "System" context.

What is Hessian?

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