A canonical Geronimus transformation for matrix orthogonal polynomials
Juan Carlos García-Ardila, Luis E. Garza, Francisco Marcellán · Linear and Multilinear Algebra · 2017
We consider matrix polynomials orthogonal with respect to a sesquilinear form such that where is a symmetric, positive definite matrix of measures supported in some infinite subset of the real line, and W(t) is a matrix polynomial of degree 1. We obtain a connection formula between the sequences of matrix polynomials orthogonal with respect to and , as well as a relation between the corresponding block Jacobi matrices. A non-symmetric sesquilinear form is also considered.