Clifford Algebras and Vector-Valued Rational Forms. I

D. E. Roberts

Abstract

We demonstrate how Clifford algebras offer a framework for the construction of vector-valued rational forms possessing features of the usual scalar theory, including three-term recurrence relations for continued fractions. The price for this advantage is that the Moore-Penrose generalized inverse is replaced by the multiplicative group inverse of a Clifford algebra. However, the connection between the new vector-valued rational forms and generalized inverse rational forms is a close one; in fact, the two forms are identical for real analytic data.