From Grassmann'S Vision To Geometric Algebra Computing
HERMANN GRASSMANN: FROM PAST TO FUTURE: GRASSMANN'S WORK IN CONTEXT(2011)
摘要
What mathematicians often call Clifford algebra is calledgeometric algebra if the focus is on the geometric meaning of the algebraic expressions and operators. Geometric algebra is a mathematical
framework to easily describe geometric concepts and oper- ations. It allows us to develop algorithms fast and in an intuitive
way. It is based on the work of Hermann Grassmann [A2] and his vision of a general mathematical language for geometry. William
Clifford combined Grassmann’s exterior algebra and Hamilton’s quaternions [Clifford 1882a, 1882b]. Pioneering work has been
done by David Hestenes, who first applied geometric algebra to problems in mechanics and physics [Hestenes and Sobczyk 1984;
Hestenes 1985].His work culminated some years ago in the invention of conformal geometric algebra [Hestenes 2001].
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