Grassmann Algebra

TheInteriorProduct.nb 44
6.15 Historical Notes
Grassmann's definition of the interior product
Grassmann and workers in the Grassmannian tradition define the interior product of two
elements as the product of one with the complement of the other, the product being either
exterior or regressive depending on which interpretation produces a non-zero result.
Furthermore, when the grades of the elements are equal, it is defined either way. This definition
involves the confusion between scalars and n-elements discussed in Chapter 5, Section 5.1
(equivalent to assuming a Euclidean metric and identifying scalars with pseudo-scalars). It is to
obviate this inconsistency and restriction on generality that the approach adopted here bases its
definition of the interior product explicitly on the regressive exterior product.
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