  Recently a spectral Favard theorem for bounded banded lower Hessenberg
matrices that admit a positive bidiagonal factorization was presented. These
type of matrices are oscillatory. In this paper the Lima-Loureiro
hypergeometric multiple orthogonal polynomials and the Jacobi-Pi\~neiro
multiple orthogonal polynomials are discussed at the light of this bidiagonal
factorization for tetradiagonal matrices. The Darboux transformations of
tetradiagonal Hessenberg matrices is studied and Christoffel formulas for the
elements of the bidiagonal factorization are given, i.e., the bidiagonal
factorization is given in terms of the recursion polynomials evaluated at the
origin.
