Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: dot product and vectors with imaginary numbers Date: Wed, 7 Jul 2010 06:41:03 +0000 (UTC) Organization: Boeing Co Lines: 24 Message-ID: <i117hv$pm4$1@fred.mathworks.com> References: <i10g08$ei8$1@fred.mathworks.com> <i10gmo$t6q$1@fred.mathworks.com> <i10m8u$lc0$1@fred.mathworks.com> <i11100$3vc$1@fred.mathworks.com> <i112tr$9df$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-03-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1278484863 26308 172.30.248.38 (7 Jul 2010 06:41:03 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Wed, 7 Jul 2010 06:41:03 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 756104 Xref: news.mathworks.com comp.soft-sys.matlab:650957 "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