Faghmous, ChadiaBouras, Mohamed CherifAli Khelil, Karima2022-05-102022-05-102019-04-23Faghmous, Chadia. Bouras, Mohamed Cherif. Ali Khelil, Karima. 2-Orthogonal Polynomials and Darboux Transforms. 3rd International Conference in Operator Theory, PDE and Applications. April 23-24- 2019. Faculty of Exact Science. Mathematics Department. University of ElOued. [visited in ../../….]. available from [copy the link here]https://dspace.univ-eloued.dz/handle/123456789/11059Working paper.3rd International Conference in Operator Theory, PDE and Applications. April 23-24- 2019. Faculty of Exact Science. Mathematics Department. University of ElOuedIn this work we present a new interpretation of Darboux transforms in the context of 2-orthogonal polynomials and nd condi- tions in order for any Darboux transform to yield a new set of 2- orthog- onal polynomials. We also introduce the LU and UL factorizations of the monic Jacobi matrix associated with a quasi-de nite linear functional de ned on the linear space of polynomials with real coe¢ cients.en2 orthogonal polynomials, linear functional, Darboux transfor- mationWorking Paper