Grassmann Algebra

ExploringCliffordAlgebra.nb 2
12.8 The Clifford Product of Orthogonal Elements
The Clifford product of totally orthogonal elements
The Clifford product of partially orthogonal elements
� Testing the formulae
12.9 The Clifford Product of Intersecting Orthogonal Elements
Orthogonal union
Orthogonal intersection
12.10 Summary of Special Cases of Clifford Products
Arbitrary elements
Arbitrary and orthogonal elements
Orthogonal elements
Calculating with Clifford products
12.11 Associativity of the Clifford Product
Associativity of orthogonal elements
A mnemonic formula for products of orthogonal elements
Associativity of non-orthogonal elements
� Testing the general associativity of the Clifford product
12.13 Clifford Algebra
Generating Clifford algebras
Real algebra
� Clifford algebras of a 1-space
12.14 Clifford Algebras of a 2-Space
� The Clifford product table in 2-space
Product tables in a 2-space with an orthogonal basis
� Case 1: �e1 � e 1 ��1, e 2 � e 2 ��1�
� Case 2: �e1 � e1 ��1, e2 � e2 ��1�
� Case 3: �e1 � e1 ��1, e2 � e2 ��1�
12.15 Clifford Algebras of a 3-Space
� The Clifford product table in 3-space
� ��3 : The Pauli algebra
� ��3 � : The Quaternions
The Complex subalgebra
� Biquaternions
12.16 Clifford Algebras of a 4-Space
� The Clifford product table in 4-space
� ��4 : The Clifford algebra of Euclidean 4-space
� ��4 � : The even Clifford algebra of Euclidean 4-space
� ��1,3 : The Dirac algebra
� ��0,4 : The Clifford algebra of complex quaternions
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