Branquinho, AmilcarFoulquié Moreno, AnaMañas Baena, Manuel Enrique2023-06-222023-06-222023-061664-236810.1007/s13324-023-00801-1https://hdl.handle.net/20.500.14352/72313CRUE-CSIC (Acuerdos Transformativos 2023) © The Author(s) 2023 Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. Amilcar Branquinho thanks Centre for Mathematics of the University of Coimbra-UIDB/00324/2020 (funded by the Portuguese Government through FCT/MCTES) and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020Ana Foulquie acknowledges Center for Research & Development in Mathematics and Applications, supported through the Portuguese Foundation for Science and Technology (FCT- Fundacao para a Ciencia e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. Manuel Manas: Thanks financial support from the Spanish "Agencia Estatal de Investigacion" research project [PGC2018-096504-B-C33], Ortogonalidad y Aproximacion: Teoria y Aplicaciones en Fisica Matematica and [PID2021- 122154NB-I00], Ortogonalidad y Aproximacion con Aplicaciones en Machine Learning y Teoria de la Probabilidad.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-Pineiro 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.engAtribución 3.0 Españahttps://creativecommons.org/licenses/by/3.0/es/journal articlehttp://dx.doi.org/10.1007/s13324-023-00801-1https://link.springer.com/open access51-73Tetradiagonal Hessenberg matricesOscillatory matricesTotally nonnegative matricesMultiple orthogonal polynomialsFavard spectral representationDarboux transformationsChristoffel formulasFísica-Modelos matemáticosFísica matemática