In the geometric algebra1 there are some problems, which not found in the literature, and I would like to share my thoughts about these now. I restrict my examination to those geometric algebras, where the starting point is a finite dimensional Euclidean vector space and the real numbers. In the Euclidean vector space an internal product is defined with an outer product generalized by Grassmann. After that, a so-called geometric product, which will be the basic operation in the geometric algebra, is defined.
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1 See for example the book of Chris Doran - Anthony Lasenby titled Geometric Algebra for Physicists;
http://www.cambridge.org/nl/academic/subjects/physics/theoretical-physics-and-mathematical-physics/geometric-algebra-physicists?format=PB
or an article titled „Imaginary Numbers are not Real — the Geometric Algebra of Spacetime” by Gull-Lasenby-Doran
http://www.researchgate.net/publication/226188504_Imaginary_numbers_are_not_realThe_geometric_algebra_of_spacetime
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