Abstract
This paper gives a concise outline for an extended, multi-dimensional number system from a component perspective. We briefly motivate such a system, sketch the associated algebra and geometry, and conclude with a connection to tensor products that shows it is reasonable, if not desirable, to add tensors of different orders.
Keywords
Get full access to this article
View all access options for this article.
References
1.
Hestenes, D.
New foundations for classical mechanics Dordrecht , Holland : D. Reidel , 1986 .
2.
Crowe, M.
A history of vector analysis: the evolution of the idea of a vectorial system . Indiana : University of Notre Dame Press , 1967 .
3.
Bayliss, WE.
(Ed.) Clifford (geometric) algebras with applications in physics, mathematics, and engineering . Boston : Birkhäuser , 1996 .
4.
Kuipers, JB
Quaternions and rotation sequences
Princeton, NJ : Princeton University Press , 1999 .
5.
Doran, CJL
, and
Lasenby, AN
Geometric algebra for physicists . Cambridge : Cambridge University Press , 2003 .
6.
De Sabbata, V.
, and
Datta, BK
Geometric algebra and applications to physics . Boca Raton, FL : CRC Press , 2007 .
7.
Vince, J.
Geometric algebra for computer graphics . London : Springer-Verlag , 2008 .
8.
Perwass, C.
Geometric algebra with applications in engineering . Berlin : Springer-Verlag , 2009 .
9.
Hestenes, D.
‘Geometric Calculus Research & Development’ , http://geocalc.clas.asu.edu/ (2007 ).
10.
Dorst, L.
,
Fontijne, D.
, and
Mann, S.
‘Geometric Algebra for Computer Science’ . http://www.geometricalgebra.net/ (2007-2009 ).
11.
Carroll, MM
Must elastic materials be hyperelastic?
Math Mech Solids
2009 ; 14 : 369 -376 .
12.
Churchill, RV
, and
Brown, JW
Complex variables and applications . New York : McGraw-Hill , 1990 .