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| 1. Physicists generally use angle brackets with a vertical bar instead of the comma: <.|.>. This is the inner product in Dirac's bra-ket notation.
2. From the footnote: "A small minority of authors impose linearity on the second coordinate instead of the first coordinate." Perhaps, if "authors" is replaced with "mathematicians". Essentially all, if not all, physics texts impose linearity on the second coordinate.
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