LINEAR TRANSFORMATIONS IN UNITARY GEOMETRIC ALGEBRA

The interpretation of complex eigenvalues of linear transformations de fined on a real geometric algebra presents problems in that their geom etric significance is dependent upon the kind of linear transformation involved, as well as the algebraic lack of universal commutivity of b ivectors. The present work shows how the machinery of geometric algebr a can be adapted to the study of complex linear operators defined on a unitary space. Whereas the well-defined geometric significance of rea l geometric algebra is not lost, the primary concern here is the study of the algebraic properties of complex eigenvalues and eigenvectors o f these operators.