Grassmann Algebra. Exploring extended vector algebra with Mathematica
John Browne
Three of the more important mathematical systems for representing the entities of contemporary
engineering and physical science are the (three-dimensional) vector algebra, the more general
tensor algebra, and geometric algebra. Grassmann algebra is more general than vector algebra,
overlaps aspects of the tensor algebra, and underpins geometric algebra. It predates all three. In this
book we will show that it is only via Grassmann algebra that many of the geometric and physical
entities commonly used in the engineering and physical sciences may be represented
mathematically in a way which correctly models their pertinent properties and leads
straightforwardly to principal results.
engineering and physical science are the (three-dimensional) vector algebra, the more general
tensor algebra, and geometric algebra. Grassmann algebra is more general than vector algebra,
overlaps aspects of the tensor algebra, and underpins geometric algebra. It predates all three. In this
book we will show that it is only via Grassmann algebra that many of the geometric and physical
entities commonly used in the engineering and physical sciences may be represented
mathematically in a way which correctly models their pertinent properties and leads
straightforwardly to principal results.
カテゴリー:
年:
2009
版:
Incomplete draft
言語:
english
ページ:
759
ファイル:
PDF, 9.57 MB
IPFS:
,
english, 2009
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