Its an easy question but still i cant seem to find the hessian matrix.

I have the following function : $$-2x^2 + \sqrt{2}xy - \frac52y^2$$

Find the hessian matrix for this function.

$$f_{11} = -4 \text{( this is correct)}$$ $$f_{12} = \sqrt2 \text{( this is wrong)}$$ $$f_{21} = \sqrt2 \text{( this is wrong)}$$ $$f_{22} = -5 \text{( this is correct)}$$

My steps were to differentiate the function in terms of $x$ and $y$. Then re differentiate in terms of $y$ to get $f_{12}$ and $x$ to get $f_{21}$.

This is simple but I can't find where I am not getting it right..

Thank you

  • $\begingroup$ What is your source for saying that these Hessian elements are wrong? Indeed, as @Siong Thye Goh states in his answer, they are correct. $\endgroup$ – Mark L. Stone Mar 17 at 16:50

The hessian is indeed

$$\begin{bmatrix}f_{xx} & f_{xy} \\ f_{yx} & f_{yy}\end{bmatrix}=\begin{bmatrix} -4 & \sqrt2 \\ \sqrt2 & -5\end{bmatrix}$$

There isn't a mistake.

Here's the result from Wolfram Alpha:

enter image description here


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