Grassmann Algebra

10 Exploring the Generalized
Grassmann Product
10.1 Introduction
10.2 Geometrically Interpreted 1-elements
Definition of the generalized product
Case Λ = 0: Reduction to the exterior product
Case 0 < Λ < Min[m, k]: Reduction to exterior and interior products
Case Λ = Min[m, k]: Reduction to the interior product
Case Min[m, k] < Λ < Max[m, k]: Reduction to zero
Case Λ = Max[m, k]: Reduction to zero
Case Λ > Max[m, k]: Undefined
10.3 The Symmetric Form of the Generalized Product
Expansion of the generalized product in terms of both factors
The quasi-commutativity of the generalized product
Expansion in terms of the other factor
10.4 Calculating with Generalized Products
� Entering a generalized product
� Reduction to interior products
� Reduction to inner products
� Example: Case Min[m, k] < Λ < Max[m, k]: Reduction to zero
10.5 The Generalized Product Theorem
The A and B forms of a generalized product
� Example: Verification of the Generalized Product Theorem
� Verification that the B form may be expanded in terms of either factor
10.6 The Zero Interior Sum Theorem
Generalized Grassmann products with the unit scalar
Generalized Grassmann products with the unit n-element
The Zero Interior Sum Theorem
� Generating the zero interior sum
10.7 The Zero Generalized Sum
The zero generalized sum conjecture
� Generating the zero generalized sum
� Exploring the conjecture
10.8 Nilpotent Generalized Products
Nilpotent products of simple elements
Nilpotent products of non-simple elements
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