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Subject: Re: dot product and vectors with imaginary numbers
Date: Wed, 7 Jul 2010 06:41:03 +0000 (UTC)
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <i112tr$9df$1@fred.mathworks.com>...
> "Matt Fig" <spamanon@yahoo.com> wrote in message <i11100$3vc$1@fred.mathworks.com>...
> 
> > 
> > 
> > Hmmmm,  I was thinking this was a Hermitian Form, as shown here (equation 2):
> > 
> > http://mathworld.wolfram.com/HermitianForm.html
> > 
> > I was taught that the second vector is conjugated in this case, so the result is the conjugate of the MATLAB definition.  Is it just convention or what? 
> 
> I don't believe there is a universal standard for fixing the first or second argument that being conjugate in the dot product, but yeah in most "classical" textbooks I read (Brezis, Rudin, Ciarley), they often gives 
> 
> <a,b> = sum(a.*conj(b))
> 
> as definition. Matlab DOT function is the opposite.
> 
> Both conventions are correct dot products so as to induce an Hilbert space as defined in a more abstract way.
>  
> Bruno

FYI, both Fortran and the BLAS routines conjugate the first, like MATLAB.

James Tursa