Orthogonal matrix polynomials and quadrature formulas Original Research Article

We prove that the nodes of a quadrature formula for a matrix weight with the highest degree of precision must necessarily be the zeros of a certain orthonormal matrix polynomial with respect to the matrix weight and the quadrature coefficients are then the coefficients in the partial fraction decomposition of the ratio between the inverse of this orthonormal matrix polynomial and the associated polynomial of the second kind. We also extend this result for quadrature formulas with degree of precision one unit smaller than the highest possible.