Talk:Geometric algebra: Difference between revisions
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Anyways... if you can figure out what it is that you want, I guess go for it... --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 15:35, 21 October 2015 (UTC)
:There is always an othonormal basis in a vector space with a scalar product. And the inner product always defines a scalar product. So these are not additional constraints. The only additional constraints I added were the vector dimension of at least five and the euclidean metric.
:I'm not sure where you are going with your suggestion of boolean addition, multiplication or modular arithmetics. I'm pretty sure such operations would not allow the inclusion of a vector space.
:You seem to keep questioning the pertinence of the axioms but again, I did not invent them. They look fine to me.--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 15:55, 21 October 2015 (UTC)
::Nothing in the text I quoted requires the existence of a scalar product. You did mention scalar product elsewhere, but not in the quoted axioms. See also: http://mathworld.wolfram.com/VectorSpace.html --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 17:37, 21 October 2015 (UTC)
:::I was referring to your mention of the orthonormal basis being a constraint to the task. The existence of a scalar product, and thus of an orthonormal basis, is a consequence of the axioms. It is thus not a constraint.--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 19:02, 21 October 2015 (UTC)
::::Sure, all vector spaces have a basis but there's nothing in those axioms that say anything about the dimension of that basis. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 20:46, 21 October 2015 (UTC)
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