My point at least was just that it’s a bad idea to use adjoint to construct a column matrix since in that case you likely didn’t intend to take an adjoint, you just wanted a certain shape.

There’s no math or physics equation here with objects transforming under an adjoint representation, it’s just a constructor.

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^* .