Direct Construction of Grassmann, Clifford and Geometric Algebras

Abstract: This is a simple way rigorously to construct Grassmann, Clifford and Geometric Algebras, allowing degenerate bilinear forms, infinite dimension, using fields or certain modules (characteristic 2 with limitation) - and characterize the algebras in a coordinate free form. The construction is done in an orthogonal basis, and the algebras characterized by universality. The basic properties with short proofs provides a clear foundation for further development of the algebras.