Geometric products: Difference between revisions
Eric Lengyel (talk | contribs) (Created page with "The ''geometric product'' is the fundamental product of geometric algebra. There are two products with symmetric properties called the geometric product and geometric antiproduct. == Geometric Product == The following Cayley table shows the geometric products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric product is the scalar basis element $$\mathbf 1$$. Cells colored yellow correspond...") |
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The following Cayley table shows the geometric products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric product is the [[scalar]] basis element $$\mathbf 1$$. | The following Cayley table shows the geometric products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric product is the [[scalar]] basis element $$\mathbf 1$$. | ||
Cells | Cells highlighted green correspond to nonzero contributions from the [[wedge product]]. | ||
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The following Cayley table shows the geometric antiproducts between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric antiproduct is the [[antiscalar]] basis element $${\large\unicode{x1D7D9}}$$. | The following Cayley table shows the geometric antiproducts between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric antiproduct is the [[antiscalar]] basis element $${\large\unicode{x1D7D9}}$$. | ||
Cells | Cells highlighted green correspond to nonzero contributions from the [[antiwedge product]]. | ||
Latest revision as of 23:06, 3 April 2024
The geometric product is the fundamental product of geometric algebra. There are two products with symmetric properties called the geometric product and geometric antiproduct.
Geometric Product
The following Cayley table shows the geometric products between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric product is the scalar basis element $$\mathbf 1$$.
Cells highlighted green correspond to nonzero contributions from the wedge product.
Geometric Antiproduct
The following Cayley table shows the geometric antiproducts between all pairs of basis elements in the 5D conformal geometric algebra $$\mathcal G_{4,1}$$. The identity of the geometric antiproduct is the antiscalar basis element $${\large\unicode{x1D7D9}}$$.
Cells highlighted green correspond to nonzero contributions from the antiwedge product.
