Grassmann Algebra

12 Exploring Clifford Algebra
12.1 Introduction
12.2 The Clifford Product
Definition of the Clifford product
� Tabulating Clifford products
� The grade of a Clifford product
� Clifford products in terms of generalized products
� Clifford products in terms of interior products
� Clifford products in terms of inner products
� Clifford products in terms of scalar products
12.3 The Reverse of an Exterior Product
Defining the reverse
� Computing the reverse
12.4 Special Cases of Clifford Products
� The Clifford product with scalars
� The Clifford product of 1-elements
The Clifford product of an m-element and a 1-element
The Clifford product of an m-element and a 2-element
� The Clifford product of two 2-elements
The Clifford product of two identical elements
12.5 Alternate Forms for the Clifford Product
Alternate expansions of the Clifford product
� The Clifford product expressed by decomposition of the first factor
Alternative expression by decomposition of the first factor
The Clifford product expressed by decomposition of the second factor
The Clifford product expressed by decomposition of both factors
12.6 Writing Down a General Clifford Product
� The form of a Clifford product expansion
� A mnemonic way to write down a general Clifford product
12.7 The Clifford Product of Intersecting Elements
General formulae for intersecting elements
Special cases of intersecting elements
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