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Yes, one may keep that in mind when working something on scratch paper. But when it’s possible for things to be complex, the standard notation is something like A^. In my opinion, it is rather sloppy to write A^T and expect the reader to substitute for the complex case. I can’t remeber where at the moment, but I have definitely seen derivations when the authors explicitly wanted A^T on a complex matrix.

You have to escape your star A^* .

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