Talk:Geometric algebra: Difference between revisions
→A possible source of confusion
(→A possible source of confusion: precision) |
|||
Line 88:
:::::::::Strictly speaking, all elements of a geometric algebra are vectors, since the whole geometric algebra has a natural vector space structure. However, the word ''vector'' is usually reserved to the elements of <math>\mathcal{V}</math>. Other elements are ''multivectors''.--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 19:38, 19 October 2015 (UTC)
:::::::::The task description does expose this if you look carefully.--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 19:41, 19 October 2015 (UTC)
::::::::::Sure, but there's nothing in the task description which supports the idea that i, j and k are not vectors. The axioms of vector spaces hold for i, j and k -- you can add them, and you can scale them and that includes scaling them by -1 which we can think of as being an inverse. You referred to them as bivectors, but the relevant definition of that term was not included in the task description.
::::::::::If it's not in the task description, and it's relevant to the task, that's a defect of the task description. You can't just refer people to some unmanageably large external context and expect that people will be able to distinguish the parts of that context which you consider relevant from the parts you consider irrelevant.
::::::::::Put differently, I do not know whether the presence of a <math>\mathcal{V}</math> within a clifford algebra excludes the existence of a different <math>\mathcal{V'}</math> from the algebra. Maybe it does, and maybe the statement "It is a known fact that if the dimension of <math>\mathcal{V}</math> is <math>n</math>, then the dimension of the algebra is <math>2^n</math>." hints at the axioms or constraints or concepts which require that. Or maybe not. I've not studied the subject enough to say for sure. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 20:15, 19 October 2015 (UTC)
== "Orthonormal basis" ==
| |||