This paper addresses some problems arising in Wiener-Hopf factorizations. The point of interest in this paper is not so much in the results which are slight generalizations of previous results, see Gohberg and Zucker [12, 13] and Zucker [18]. Rather, the main interest is in the different, functional oriented, technique used which allows the establishing of a clearer connection between factorization theory and geometry. That such a connection exists is known to every student of a linear algebra course. Indeed, the computation of a 1-dimensional invariant subspace of a finite dimensional linear transformation via the computation of an eigenvalue and a corresponding eigenvector lead to the factorization of the linear pencil λI – A.