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We have to use the Hessian to calculate the second order derivatives of a function. While that is okay if the function is mapped from $\mathbb{R}^n$ to $\mathbb{R}$, how does one proceed if it is mapped from $\mathbb{R}^n \longrightarrow \mathbb{R}^m$, where $m > 1$? How does one take the derivative of f with respect to each variable when f is itself in more than one dimension?

For example, if there is a function f : $\mathbb{R}^2 \longrightarrow \mathbb{R}^3$ with $(x,y)$ mapped to $(x^2 + y, y^3, \cos(y))$, how does one calculate the Hessian?

Thank you

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    Do it component-wise.2012-07-11
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    Then how does the hessian look like? Normally it would look like this: [del^2(f)/delx^2 del^2(f)/delx dely;del^2(f)/dely^2 del^2(f)/delx dely ] . Now how will it look like?2012-07-11

2 Answers 2