Grassmann algebra

Abstract

This chapter presents a systematic account of Grassmann (exterior) algebra, with emphasis on aspects useful for geometric measure theory, and with strict adherence to the principles of naturality. The reader is assumed to be familiar with the category of vector spaces and linear maps, but no knowledge of multilinear algebra (or determinants) is presupposed. The field of scalars will be the field R of real numbers, except where another field is explicitly specified. Of course much of the theory is applicable more generally, even to modules.