Talk:Geometric algebra: Difference between revisions
→J's orthonormality expression.: new section
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:::::::::So... let's review: a quaternion consists of four orthogonal components. What you term the "scalar part" is a part of an orthonormal basis for quaternions. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 18:30, 17 October 2015 (UTC)
::::::::::A scalar is not orthogonal to a vector.--[[User:Grondilu|Grondilu]] ([[User talk:Grondilu|talk]]) 18:40, 17 October 2015 (UTC)
== J's orthonormality expression. ==
The J expression <code>0 1 2 3 dot&e"0/0 1 2 3</code> generates a table of 16 dot products.
Breaking this down:
The left argument is 0 1 2 3, and the right argument is 0 1 2 3. each row corresponds to an item from the left argument (the first row corresponding to the first item from the left argument, the last row corresponding to the last item from the left argument - in other words, rows in the result are in the same order as items in the left argument. Likewise columns in the result correspond to items from the right argument.
In each case, the value in the result is the result of (e left_item) dot (e right_item).
As the result is an identity matrix, we can see that we have an orthonormal basis.
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