O'Reilly logo

A Course in Mathematical Analysis by D. J. H. Garling

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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: ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required