Wedge products: Difference between revisions

Latest revision as of 03:18, 6 August 2023

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-The ''exterior product'' is the fundamental product of Grassmann Algebra, and it forms part of the [[geometric product]] in geometric algebra. There are two products with symmetric properties called the exterior product and exterior antiproduct.
+#REDIRECT [[Exterior products]]
-== Exterior Product ==
-The following Cayley table shows the exterior products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$.
-[[Image:WedgeProduct.svg|1440px]]
-== Exterior Antiproduct ==
-The following Cayley table shows the exterior antiproducts between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$.
-[[Image:AntiwedgeProduct.svg|1440px]]
-== De Morgan Laws ==
-We can express the product and antiproduct in terms of each other through an analog of De Morgan's laws as follows.
-:$$\overline{\mathbf a \wedge \mathbf b} = \overline{\mathbf{a\vphantom{b}}} \vee \overline{\mathbf b}$$
-:$$\overline{\mathbf a \vee \mathbf b} = \overline{\mathbf{a\vphantom{b}}} \wedge \overline{\mathbf b}$$
-:$$\underline{\mathbf a \wedge \mathbf b} = \underline{\mathbf{a\vphantom{b}}} \vee \underline{\mathbf b}$$
-:$$\underline{\mathbf a \vee \mathbf b} = \underline{\mathbf{a\vphantom{b}}} \wedge \underline{\mathbf b}$$
-== See Also ==
-* [[Geometric products]]
-* [[Dot products]]
-* [[Duals]]