Geometric algebra is the Clifford algebra generated by a vector space 
with quadratic form 
, subject to
for every 
.
For an inner product space, the geometric product
of vectors decomposes as
where the symmetric part is the dot product and the antisymmetric part is the wedge product. Scalars,
vectors, bivectors, and elements
of higher grade therefore belong to a single associative
algebra.
See also
Clifford Algebra,
Dot Product,
Exterior Algebra,
Wedge
Product
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References
Doran, C. and Lasenby, A. Geometric
Algebra for Physicists. Cambridge, England: Cambridge University Press, 2003.
Cite this as:
Weisstein, Eric W. "Geometric Algebra."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeometricAlgebra.html
Subject classifications
