Let's say I have:
$$ U = \begin{bmatrix} 1 &2 &3 \\ 0 &1 &1.3 \\ 0& 0 & 1 \end{bmatrix} $$ $$ L = \begin{bmatrix} 10 & 0 & 0 \\ 40 & -30 & 0 \\ 10 & 30 & 10 \end{bmatrix} $$
I want to show how I have calculated the determinant (taking the product of the diagonal elements of $U$ multiplied by the product of the diagonal product of $L$) in an elegant way. Does the following represent this:
$$Det(x) = \prod_{i=1}^{n} diag(U) \cdot diag(L)$$
I am sure there is a more "elegant" and "optimal" way to represent what I'm trying to do.