Below is an awkward algorithm to solve the above problem.

ComputeSumLowerTriangular$($L$,$n$)$

inputs: L is an nxn matrix. n is the dimension of the matrix

output: a real number equal to

$1$: sum $=0$

$2$: for i $=$ n to $1$

$3$: psum $=0$

$4$: for j $=1$ to i

$5$: psum $=$ psum $+$ L$[$i$,$j$]$

$6$: sum $=$ sum $+$psum

$7$: return sum