Abstract
are considered for differential polynomial matrices P having real meromorphic coefficients. The main results are: the lattice of possible solution spaces of such equations having singularities only in a prescribed set is antiisomorphic to the lattice of the corresponding matrix left principal ideals. The solution spaces of equal dimension can be classified via differential isomorphisms. The equivalence classes correspond to certain matrix classes defined in algebraic terms. In case no essential singularities are present the results are in [6]. The problem of identifying appropriate representatives for the classes is only solved in the nonsingular case. The restriction to real meromorphic coefficients is due to system theoretic applications (see references in [6]) where the coefficients represent time functions, though more general complex coefficients would be possible.
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