Talk:Geometric algebra: Difference between revisions
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:::From a vector space of arbitrary dimension (but at least 3), you can use the geometric product, not the scalar product, to create three bivectors i, j, k such that the subalgebra generated by (1, i, j, k) is isomorphic to the quaternion field. I think that's basically what the task description says. Maybe I could be a bit more verbose, but I think that is not necessary.--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 23:07, 17 October 2015 (UTC) |
:::From a vector space of arbitrary dimension (but at least 3), you can use the geometric product, not the scalar product, to create three bivectors i, j, k such that the subalgebra generated by (1, i, j, k) is isomorphic to the quaternion field. I think that's basically what the task description says. Maybe I could be a bit more verbose, but I think that is not necessary.--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 23:07, 17 October 2015 (UTC) |
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:::: The trick, here, seems to be that in this context we use multiple conflicting concepts of the term "dimension" and, for related terms such as "scalar" and "vector". A thorough exposition would detail each of these uses and show - ideally through concrete examples - how each of them is relevant to the implementation, as well as how each of these uses is different from the other uses of the same word, and perhaps the phrasing conventions we should be using to distinguish between these cases. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 17:55, 19 October 2015 (UTC) |
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== The J solution might be correct but too small == |
== The J solution might be correct but too small == |
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