Necessary And Sufficient Conditions For Existence of the LU Factorization of an Arbitrary Matrix

Pavel Okunev, Charles R. Johnson

If $A$ is an n-by-n matrix over a field $F$ ($A\in M_n(F)$), then $A$ is said to ``have an LU factorization'' if there exists a lower triangular matrix $L\in M_n(F)$ and an upp…