When I normally think about a second derivative in the 1D case, I would just see it as a scalar. It was surprising to me that the second derivative is actually all possible combinations of derivatives, not just a vector of the second derivates with respect to each variable, as the gradient is. But thinking about it in terms of the curvature of a surface helps!
keenan
@ngandhi Yes, this is a good point. And in general, if you want to know about all possible derivatives of order $n$ you will have a tensor of rank $n$.
When I normally think about a second derivative in the 1D case, I would just see it as a scalar. It was surprising to me that the second derivative is actually all possible combinations of derivatives, not just a vector of the second derivates with respect to each variable, as the gradient is. But thinking about it in terms of the curvature of a surface helps!
@ngandhi Yes, this is a good point. And in general, if you want to know about all possible derivatives of order $n$ you will have a tensor of rank $n$.