An algebraic characterization of the bilinear relations of the matrix hierarchy associated with a commutative algebra of k×k-matrices

In this paper we give a purely algebraic set-up for the equations of the matrix hierarchy that can be associated to a maximal commutative subalgebra of the k×k-matrices. Besides that it gives you a proper framework for the description of the linearization and the Lax form of the hierarchy, it enables you also to give an algebraic characterization of the dual wavefunctions of the matrix hierarchy and this leads to an algebraic interpretation of the bilinear form of this system of nonlinear equations