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$\newcommand{\lrank}{\operatorname{lrank}}$ $\newcommand{\rank}{\operatorname{rank}}$ Given a matrix $A$, we can define its Hamming weight, $w(A)$, as the number of non-zero elements in it. Now, given ...

How to study the decomposition of a square matrix into a product of sparse matrices? There are no restrictions on the number of matrices in the product, but the fewer the better.