Quasicomplete factorizations of rational matrix functions (Q1378071)

The author shows that any \(n\times n\) rational matrix function \(W\) which is analytic at infinity with value \(W(\infty)= I_n\) is the product \(W= W_1W_2\dots W_\rho\) of rational matrix functions \(W_1,W_2,\cdots,W_\rho\) of McMillan dergree one. Furthermore, such a factorization can be established with a number of factors not exceeding \(2\delta(W)- 1\), where \(\delta(W)\) denotes the McMillan degree of \(W\).