Your notation is a little strange w.r.t. to the last (vector e with upper arrow)_k then formally it must be a "tensor" with components e_(mk) ("arrow" and "index"). But the result is formally correct ;-) I would suggest to state the the "components" (axb)_k=ε_(ijk)a_(i)b_(j)
yea I guess lol I just thought it was understood that e_i were the basis vectors and I didn’t like just how the bf looked lol
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(bold e)_1=bold i,
(bold e)_2=bold j,
(bold e)_3=bold k,pic.twitter.com/0XMHzTWpcT
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All is a matter of "labelling and convention(s)" ;-) spacetime (flat/curved), internal (e.g. SU(n) etc.) indices, spinor, here with Einstein summation convention and sometimes without this convention.
End of conversation
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