> For a complex square matrix the genuine  adjoint is denoted A^* and is
> the conjugate transpose.  That is a special case of the adjoint of a
> linear operator on an inner product space (in the case of C^n with the
> standard inner product).

That's what I thought, too.  We should definitely change this.

An extremely non-random sample of linear algebra texts in my office
suggests this is the usual use in undergraduate texts.

> I support your proposal but it would have to be very well documented.
> We already have the problem, for those wanting to use Sage to teach
> linear algebra, that it uses the Magma convention where matrices act
> on the right on row vectors instead of the more common convention in
> textbooks of a left action on column vectors.  This is potentially
> another situation like that...

Having not used Sage to teach linear algebra, I haven't run into
that... yet.  But probably the current situation with the adjoint is
the reverse situation (i.e., current behavior is not the usual
convention for teaching).

With respect to 2., maybe a search of all sagenb worksheets for uses
of adjoint would be helpful in ascertaining things... or it could be a
backwards-incompatible change in time for 5.0.  Whenever that
happens.  But I don't think there is a good way to come up with an
interim solution, short of adding a keyword nonclassical=True, which
seems extremely onerous!

- kcrisman

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