  Matrix valued Laguerre polynomials are introduced via a matrix weight
function involving several degrees of freedom using the matrix nature. Under
suitable conditions on the parameters the matrix weight function satisfies
matrix Pearson equations, which allow to introduce shift operators for these
polynomials. The shift operators lead to explicit expressions for the
structures of these matrix valued Laguerre polynomials, such as a Rodrigues
formula, the coefficients in the three-term recurrence, differential operators,
and expansion formulas.
