Geometric algebra and geometric calculus can be used to unify and sometimes simplify a host of mathematical concepts which one has already encountered elsewhere. If, for example, one thinks of complex numbers or differential forms, then one discovers, there they are already, lurking in GA and GC along with a lot of other creatures, familiar and unfamiliar.

Here we give a link to a small paper which exhibits the Hodge star operator in a form which seems perhaps simpler than that usually encountered in the literature. Further, the Hodge star operator is usually defined by a condition it must satisfy. Here, we give an explicit definition.

Here is the link: On the Definition of the Hodge Star Operator within Geometric Algebra.