Sign determinancy in LU factorization of P-matrices Original Research Article

For an n-by-nP-matrixA = [aij] having LU factorization A = LU with U = [uij], we determine combinatorial circumstances for which uij is unambiguously signed for a given pair i ≤ j, or all such pairs, and give corresponding results for L. A qualitative P-matrix is a sign nonsingular matrix with all diagonal entries positive. For such a matrix A, we give additional sufficient conditions for an entry uij or the matrix U to be unambiguous. If A is a qualitative P-matrix with A−1 unambiguously signed, we prove that the matrices L, U, L−1, and U−1 are all unambiguous.