TABLE OF CONTENTS Hermann Gunther Grassmann was born in 1809 near the border of Germany and Poland in a town called Stettin. He discovered an algebra of geometry that includes vectors. His algebra subsumes the common form of algebra we all learn in high school. During his lifetime he received very little recognition for his discovery. William Kingdon discovered Grassmann's work about 1877, the year Grassmann died. Clifford's algebras are still used today for manipulation of vectors and linear mathematical systems.
A brief introduction to Grassmann algebra is presented in this appendix. The information included here is largely based on reference [1]. For those desiring more detailed information references [2 21] are recommended.
Grassmann's algebra is a theory of "extension," with the fundamental product operation being the exterior product. In this algebra, addition, negation, and multiplication by a scalar carry the same meaning as in the normal mathematics we are all familiar with. The product operation, however, is different.
The constructs of this algebra allow manipulation of geometric objects algebraically. That is, lines can be constructed from points, and lines can be manipulated. Planes can be constructed from lines and/or points and these planes can be manipulated algebraically. Higher forms of geometric shapes can be constructed and manipulated just as easily. Such manipulation includes functions such as finding the intersection of two or more geometric objects.
The common 3-D vectors are one form of geometric shapes that can be built in the algebra. Vectors such as these, of course,...
