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Mar 5, 2020 at 23:45 vote accept Jake Wetlock
Mar 5, 2020 at 20:48 comment added Matthew Daws Yes, that is completely right, and is (I think!) a very nice observation. But see also my edit to my answer.
Mar 5, 2020 at 20:47 history edited Matthew Daws CC BY-SA 4.0
Add a new argument.
Mar 5, 2020 at 19:08 comment added Jake Wetlock So in short, the fact that we choose the inner product to be conjugate linear in the first variable makes left multiplication the "natural choice". Hence I would guess that if we were to choose the inner product to be conjugate linear in the second variable, that is $\langle a,b\rangle := \phi(ab^*)$ then right multiplication would be the natural choice?
Mar 5, 2020 at 18:36 history edited Matthew Daws CC BY-SA 4.0
added 23 characters in body
Mar 5, 2020 at 18:31 history answered Matthew Daws CC BY-SA 4.0