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I came upon an interesting problem. Suppose you have three vectors $\psi=(a, b)$, $\phi=(c,d)$ such that their components do not commute: $ac\neq ca$, $bd \neq db$ etc. (in general the vectors may have more than two components) How do you perform the inner product ψ.φ?

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    $\begingroup$ You could use Inner[] with NonCommutativeMultiply[]... $\endgroup$ – J. M.'s ennui Dec 23 '20 at 11:03
  • $\begingroup$ @J.M.'sdiscontentment Inner allows the calculation of the inner product of only two vectors. If I need the inner product of 4 or 6? $\endgroup$ – geom Dec 23 '20 at 12:52
  • $\begingroup$ The inner product is a scalar and can be factored out. So for e.g. 4 vectors it would read: v1.v2 v3.v4 $\endgroup$ – Daniel Huber Dec 23 '20 at 13:00
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    $\begingroup$ By "." I mean any inner product you are using. $\endgroup$ – Daniel Huber Dec 23 '20 at 13:36
  • $\begingroup$ How exactly do you define the inner product of three or more vectors? $\endgroup$ – J. M.'s ennui Dec 23 '20 at 14:19

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