In wolframpage there is follows definition for shape operator in a given point by vector(adsbygoogle = window.adsbygoogle || []).push({}); v:

I think that this equation means: [tex]S(\vec{v})=-\frac{d\hat{n}}{d \vec{v}}[/tex] correct, or not?

If yes, of according with the matrix calculus (https://en.wikipedia.org/wiki/Matrix_derivative#Numerator-layout_notation) the derivative of a vector in the space wrt another vector in the space results in a 3x3 matrix:

But, the shape operator is a2x2 matrix. Conclusion, there is something wrong in my interpretation, what is?

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# Definition for shape operator

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