**Appendix C**

Exterior algebras and the cross product

**C.1 Exterior algebras**

Suppose that *E* is a real vector space. An element of *E*, a vector, can be considered to have magnitude and direction. In the same way, if *x* and *y* are two vectors in *E* then they somehow relate to an area in span (*x, y*). If we wish to make this more specific, we certainly require that the area should be zero if and only if *x* and *y* are linearly dependent. A similar remark applies to higher dimensions. We wish to develop these ideas algebraically.

A finite-dimensional (associative) real *algebra* (*A, *) is a finite-dimensional real vector space equipped with a law of composition: ...

Start Free Trial

No credit card required