Confusion related to calculation of Hessian and notation

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I was reading this paper where they have calculate the gradient and hessian of a function as

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I didn't get what the cross sign means here. Further I am confused about the second row first column term of the hessian. I think it should have been $2Sxx\Theta\Lambda^{-1}\Lambda^{-1}$. However, the results are in different order in the paper. The same is the case with the others like in the 2nd row 2nd column term, it should have been $2Sxx\Lambda^{-1}$

Any guidance?