Long division for Laurent series matrices and the optimal assignment problem Original Research Article

We present a necessary and sufficient condition to represent a Laurent series matrix A(x) as a product image where image is a Laurent series matrix whose leading scalar matrix is nonsingular and U(x) and V(x) are diagonal matrices whose nonzero entries are powers of x. If A(x) can be written in this form, then the matrix equation A(x)Y(x) = B(x) can be solved by long division. Our result relies on a classical theorem on optimal assignments.