Full rank factorization in quasi-LDU form of totally nonpositive rectangular matrices

Let A = (a(ij)) is an element of R-nxm be a totally nonpositive matrix with rank(A) = r <= min{n, m} and a(11) = 0. In this paper we obtain a characterization in terms of the full rank factorization in quasi-LDU form, that is, A = (L) over tilde DU where (L) over tilde is an element of R-nxr is a block lower echelon matrix, U is an element of R-rxm is a unit upper echelon totally positive matrix and D is an element of R-rxr is a diagonal matrix, with rank((L) over tilde) = rank(U) = rank(D) = r. We use this quasi-LDU decomposition to construct the quasi-bidiagonal factorization of A. Moreover, some properties about these matrices are studied. (C) 2013 Elsevier Inc. All rights reserved.This research was supported by the Spanish DGI grant MTM2010-18228.Cantó Colomina, R.; Ricarte Benedito, B.; Urbano Salvador, AM. (2014). Full rank factorization in quasi-LDU form of totally nonpositive rectangular matrices. Linear Algebra and its Applications. 440:61-82. doi:10.1016/j.laa.2013.11.002S618244