SUCCESSIVELY ORDERED ELEMENTARY BIDIAGONAL FACTORIZATION.

Let D be a diagonal matrix and E_ij denote the n-by-n matrix with a 1 in entry (i,j) and 0 in every other entry. An n-by-n matrix A has a successively ordered elementary bidiagonal (SEB) factorization if it can be factored as [This symbol cannot be presented in ASCII format] in which L_j(s_jk) = I + s_jkE_{j,j -1} and U_j(t_kj) = I + t_kjE_{j -1,j} for some scalars s_jk,t_kj. Note that some of the parameters s_jk,t_kj may be zero, and the order of the bidiagonal factors is fixed. If this factorization corresponds to reduction of A to D via successive row/column operations in the specified order, it is called an elimination SEB factorization. New rank conditions are formulated that are proved to be necessary and sufficient for matrix A to have such a factorization. These conditions are related to known but more restrictive properties that ensure a bidiagonal factorization as above, but with all parameters s_jk,t_kj nonzero. [ABSTRACT FROM AUTHOR]