# Hessian Matrix Values

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

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

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