Full rank factorization in echelon form of totally nonpositive (negative) rectangular matrices
A real matrix is called totally nonpositive (negative) if every minor is nonpositive (negative). Motivated by the work of \textit{M. Gasca} and \textit{J. M. Peña} [Linear Algebra Appl. 165, 25--44 (1992; Zbl 0749.15010) and SIAM J. Matrix Anal. Appl. 25, No.~4, 986--994 (2004; Zbl 1066.65032)] on a variant of the Neville elimination process (the so-called quasi-Neville), the authors derive a characterization of totally negative matrices in terms of their full rank factorization in echelon form. Moreover, they use this factorization to reduce the number of minors to be checked in order to decide the totally negativity of rectangular matrices. The totally nonpositive case is considered under some restrictions. Several examples are considered.
totally positive and strictly totally positive matrices
totally nonpositive and totally negative matrices
scientific article; zbMATH DE number 5614899