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From: James Tursa on 7 Jul 2010 04:27
"James Tursa" <aclassyguy_with_a_k_not_a_c(a)hotmail.com> wrote in message <i11d60$rqk$1(a)fred.mathworks.com>...
> "James Tursa" <aclassyguy_with_a_k_not_a_c(a)hotmail.com> wrote in message <i117hv$pm4$1(a)fred.mathworks.com>...
> >
> > FYI, both Fortran and the BLAS routines conjugate the first, like MATLAB.
>
> And another "conjugate the first" site:
>
> http://people.ccmr.cornell.edu/~muchomas/8.04/1997/ps6/node3.html

And another one:

http://web.mit.edu/18.06/www/Fall07/operators.pdf

If you think of vectors as column vectors, then the dot product works out nicely as x^H * x, rather than writing x^T * conj(x), as the last article points out. Maybe this had something to do with why Fortran (and the follow on BLAS interface and MATLAB) chose to conjugate the first instead of the second. I don't really know. Maybe a post to the Fortran newsgroup is in order.

James Tursa
From: James Tursa on 7 Jul 2010 04:37
"James Tursa" <aclassyguy_with_a_k_not_a_c(a)hotmail.com> wrote in message <i11dop$510$1(a)fred.mathworks.com>...
> "James Tursa" <aclassyguy_with_a_k_not_a_c(a)hotmail.com> wrote in message <i11d60$rqk$1(a)fred.mathworks.com>...
> > "James Tursa" <aclassyguy_with_a_k_not_a_c(a)hotmail.com> wrote in message <i117hv$pm4$1(a)fred.mathworks.com>...
> > >
> > > FYI, both Fortran and the BLAS routines conjugate the first, like MATLAB.
> >
> > And another "conjugate the first" site:
> >
> > http://people.ccmr.cornell.edu/~muchomas/8.04/1997/ps6/node3.html
>
> And another one:
>
> http://web.mit.edu/18.06/www/Fall07/operators.pdf
>
> If you think of vectors as column vectors, then the dot product works out nicely as x^H * x, rather than writing x^T * conj(x), as the last article points out. Maybe this had something to do with why Fortran (and the follow on BLAS interface and MATLAB) chose to conjugate the first instead of the second. I don't really know. Maybe a post to the Fortran newsgroup is in order.

And it also appears that one of the technology labs at Indiana University is defining C++ vector operations code that has first conjugated:

http://osl.iu.edu/research/mtl/mtl4/doc/namespacemtl_1_1vector.html#_details

So it appears that the many textbooks and online "math" sites have the second conjugated, while computer languages have the first conjugated (maybe everybody is just following Fortran). I would be curious to know if there are any computer languages that have the second conjugated.

James Tursa
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