I have the following identity:
$$L=(I-A)^TD^{-1} (I-A),$$
where $I$ is the identity matrix, $A$ is a $n \times n$ lower triangular matrix with no more than $m \ll n$ non-zero elements in each row and $D$ is a $n \times n$ diagonal matrix.
I was given the task of showing that $L$ is a sparse matrix, finding the elements $L_{ij}$ explicitly in terms of $A$ and $D$, proving that most of the $L$ entries are zeros. Any hint about how to do that?