  This paper is devoted to characterizations classical orthogonal polynomials
on quadratic lattices by using a matrix approach. In this form we recover the
Hahn, Geronimus, Tricomi and Bochner type characterizations of classical
orthogonal polynomials on quadratic lattices. Moreover a new characterization
is also presented. From the Bochner type characterization we derive the
three-term recurrence relation coefficients for these polynomials.
