On Laguerre-Sobolev matrix orthogonal polynomials

In this manuscript, we study some algebraic and differential properties of matrix orthogonal polynomials with respect to the Laguerre-Sobolev right sesquilinear form defined by {formula presented} where W_L^A (x) = e^{-λ x} x^A is the Laguerre matrix weight, W is some matrix weight, p and q are the matrix polynomials, M and A are the matrices such that M is non-singular and A satisfies a spectral condition, and λ is a complex number with positive real part.