From Unoriented Subspaces to Blade Operators

Abstract

Projection operators are used to represent unoriented subspaces, thus providing a framework to potentially solve problems (such as the general meet and join) that do not have oriented solutions. The potential is made reality by using an additional derived product called the Delta product (which is the highest grade part of the geometric product of two blades) for Euclidean metrics. The results are even more applicable because a general translation technique (a LIFT to a different metric) is presented that makes solutions of some problems translatable from one metric to another. In particular this makes the meet and join computable regardless of incidence properties and even in degenerate metrics.