Generalized totally positive matrices (Q1971037)

A matrix over a ring with identity and a positive part is called generalized totally positive (GTP) if the Schur complements are positive in all nested sequences of so-called relevant submatrices, i.e. ones having either the first \(k\) rows and \(k\) consecutive columns, or \(k\) consecutive rows and the first \(k\) columns. The authors prove, among other things, that a square matrix is GTP iff it admits a certain factorization with bidiagonal-type factors and certain invertible entries, and that the product of square GTP-matrices is again GTP.