Branquinho, A.Marcellán, F.Mendes, A.2025-11-052025-11-052009-10-12Branquinho, Amílcar & Marcellán, Francisco & Mendes, A.. (2009). Vector Interpretation of the Matrix Orthogonality on the Real Line. Acta Applicandae Mathematicae. DOI: https://doi.org/112. 10.1007/s10440-010-9577-3.0167-8019http://hdl.handle.net/10400.8/14518Fonte: https://arxiv.org/abs/0910.1737In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation allows us to study a non-symmetric case of the matrix orthogonality. We also prove that our systems of polynomials are indeed orthonormal with respect to a complex measure of orthogonality. Approximation problems of Hermite-Padé type are also discussed. Finally, a Markov's type theorem is presented.engMatrix orthogonal polynomialsproblems of Hermite-Pad´elinear func- tionalrecurrence relationtridiagonal operatorFavard theoremasymptotic resultsNevai classjournal article10.1007/s10440-010-9577-31572-9036