  The properties of matrix valued polynomials generated by the scalar-type
Rodrigues' formulas are analyzed. A general representation of these polynomials
is found in terms of products of simple differential operators. The recurrence
relations, leading coefficients, completeness are established, as well as, in
the commutative case, the second order equations for which these polynomials
are eigenfunctions and the corresponding eigenvalues, and ladder operators.
  The conjecture of Duran and Grunbaum that if the weights are self-adjoint and
positive semidefinite then they are necessarily of scalar type is proved for
Q(x)=x and Q(x)=x^2-1 in dimension two, and for any dimension under genericity
assumptions.
  Commutative classes of quasi-orthogonal polynomials are found, which satisfy
all the properties usually associated to orthogonal polynomials.
