Hermann Günter Grassmann (1800 Stettin - 1877 Stettin)

Grassmann introduced the exterior algebras. Say for R3: Generating elements: x, y, z Relations: x2 = 0, z2 = 0, z2 = 0. yx = -xy, xz = -zx, yz = -zy Altogether we obtain an 8-dimensional algebra, with basis 1, x, y, z, xy, xz, yz, xyz; but usually one writes these elements in the form What is the importance of the exterior algebras ? Foundation of vector calculus In particular: of the "determinants" They are used for defining "differential forms" Exterior algebras are needed in geometry and in analysis!