A contribution to quasi-orthogonal polynomials and associated polynomials

In this paper, we study the quasi-orthogonality of polynomials and their associated polynomials. First we give a connection between these quasi-orthogonal polynomials and linear algebra. Then we use this connection to generalize some results about the location of their zeros and we also give new results. These generalizations and the new results are obtained by a different approach and without using results such as the Christoffel-Darboux's formula.