TANGENT SPACES OF RATIONAL MATRIX FUNCTIONS

We consider the task of determining tangent spaces for classes of rati onal matrix valued functions. Our analysis is based on methods from co ntrol theory, and in particular the theory of polynomial models. Expli cit descriptions of tangent spaces of rational transfer functions, sta ble rational transfer functions, rational inner functions, and symmetr ic rational transfer functions are obtained. Moreover, a new proof of Delchamps's decomposition formula for the tangent bundle of rational t ransfer functions is given. A Riemannian metric as well as a symplecti c structure is defined. (C) 1998 Elsevier Science Inc.