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We study Jordan types of linear forms for graded Artinian Gorenstein algebrashaving arbitrary codimension. We introduce rank matrices of linear forms forsuch algebras that represent the ranks of multiplication maps in variousdegrees. We show that there is a 1-1 correspondence between rank matrices andJordan degree types. For Artinian Gorenstein algebras with codimension three weclassify all rank matrices that occur for linear forms with vanishing thirdpower. As a consequence, we show for such algebras that the possible Jordantypes with parts of length at most four are uniquely determined by at mostthree parameters.

Jordan types with small parts for Artinian Gorenstein algebras of codimension three