Bidiagonal factorizations and quasi-oscillatory rectangular matrices

A real matrix A, of size m×n, is called totally nonnegative (totally positive) if all its minors are nonnegative (positive). A variant of the Neville elimination process is studied in relation to the existence of a totally nonnegative elementary bidiagonal factorization of A. The class of quasi- oscillatory rectangular matrices, which in the square case contains the oscillatory matrices, is introduced and a characterization of this class of matrices, by incorporating bidiagonal factorization, is showed.