  We study Jordan types of linear forms for graded Artinian Gorenstein algebras
having arbitrary codimension. We introduce rank matrices of linear forms for
such algebras that represent the ranks of multiplication maps in various
degrees. We show that there is a 1-1 correspondence between rank matrices and
Jordan degree types. For Artinian Gorenstein algebras with codimension three we
classify all rank matrices that occur for linear forms with vanishing third
power. As a consequence, we show for such algebras that the possible Jordan
types with parts of length at most four are uniquely determined by at most
three parameters.
