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February 26th, 2014, 06:07 AM   #1
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Definition for shape operator

In wolframpage there is follows definition for shape operator in a given point by vector v:

I think that this equation means: correct, or not?

If yes, of according with the matrix calculus ( the derivative of a vector in the space wrt another vector in the space results in a 3x3 matrix:

But, the shape operator is a 2x2 matrix. Conclusion, there is something wrong in my interpretation, what is?
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