LU factorization of a 0-1 matrix I have a rather naive question on LU factorization which probably should be easy to answer. Say I have a matrix with entries only from $\{0,1\}$. When can we expect to get an LU factorization of such a matrix(whenever it exists) with entries $(a)$ from integers? $(b)$ from $\{-1,0,+1\}$?
No. Consider the 4-by-4 matrix below.

 0     1     1     1
 1     0     1     1
 0     0     0     1
 1     1     0     1