A factorization of totally nonsingular matrices over a ring with identity Original Research Article

We say that a rectangular matrix over a ring with identity is totally nonsingular (TNS) if for all k, all its relevant submatrices, either having k consecutive- rows and the first k columns, or k consecutive- columns and the first k rows, are invertible. We prove that a matrix is TNS if and only if it admits a certain factorization with bidiagonal-type factors and certain invertible entries. This approach generalizes the Loewner–Neville factorization usually applied to totally positive matrices.