> I tend to agree with not using the complex conjugate for vecmat, but would
> prefer having
> separate functions for that that make it explicit in the name. I also note
> that mathematicians
> use sesquilinear forms, which have the vector conjugate on the other side, so
> there are
> different conventions. I prefer the Dirac convention myself, but many
> mathematical methods
> texts use the opposite. It is tricky for the teacher in introductory courses,
> right up there with
> vectors being called contravariant when they are actually covariant (the
> coefficients are
> contravariant). Anyway, I think having the convention explicit in the name
> will avoid confusion.
Hi Chuck,
Indeed, which argument to conjugate seems not generally agreed on --
definitely found wikipedia pages using both convention! But I think
numpy made the choice with vdot and vecdot, so that seems mostly a
matter of documentation.
I'm slightly confused whether or not you agree that the complex
conjugate is useful, but can see your point of a name that makes it
clear. Or perhaps one could have a wrapper function that let's one
switch between conjugating the vector or not?
One thing perhaps worth mentioning is that if we decide that vecmat does
conjugate, the non-conjugating version can still trivially be done by a
transpose using matvec(matrix.mT, vector) [1], while if vecmat does not
conjugate by default, getting the conjugate version using the "obvious"
vecmat(vector.conj(), matrix) implies a potentially costly copy of
the whole vector array. (This can be avoided using the much less
obvious np.vecdot(vec[..., np.newaxis, :], mat.mT), but I'm not sure
that one really wants to suggest that...)
More generally, in my own experience working with complex matrices and
vectors, just about anytime one needs a transpose, a conjugate is
generally needed too.
All the best,
Marten
[1] Indeed, the implementation of vecmat uses the matvec loops with the
matrix transposed for all but the complex numbers.
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