Re: [Getfem-users] vector product identity

[Renard Yves]

I can, nevertheless, propose the following proof

for v = (Ma) x (Mb) and M invertible one has
v_i = det(Ma; Mb; ei) = det(M) det(a,b,M^(-1)e_i)
    = det(M) (a x b).(M^(-1)e_i)
    = det(M) ei^T M^(-T) . (a x b)
which can be rewritten

v = det(M) M^(-T) (a x b)

Yves.



Roman Putanowicz <address@hidden> a écrit :

> Dear All,
> Please take my sincere apologies for the Polish post. I've must be to tired
> and instead to our internal mailing list I have posted it to getfem :).
> I have made in past all sorts of mistakes but this is the first one of this
> kind.
>
> Regards,
>
> Roman
> > Dear Roman,
> >
> > I just want to draw your attention that you're posting in Polish on getfem
> > mail list.
> > (Although as an Ukrainian I understand some stuff, but not good enough :)
> >  ).
> >
> > Best regards,
> >                            Andriy
> >
> > 2010/9/18 Roman Putanowicz <address@hidden>
> >
> > > Witam,
> > >
> > > Czy spotkali?cie si? mo?e gdzie? z dowodem poni?szej to?samo?ci:
> > >
> > >   (Ma) x (Mb) = det(M) M^(-T) (a x b)
> > >
> > > gdzie M macierz nieosobliwa, a,b -wektory, 'x' oznacza iloczyn wektorowy.
> > > Mo?na pokaza?, ?e powy?sze jest prawdziwe transformuj?c uk?ad  
> > wspó?rz?dnych
> > > do uk?adu w?asnego macierzy M ale jako? mi sie ten dowód nie podoba.
> > >
> > > Do czego mi to potrzebne? Mo?na to wykorzysta? wyprowadzaj?c wzór na
> > > transformacj? elementu obj?to?ci.
> > >
> > > Pozdr,
> > >
> > > Romek
> > > --
> > > Roman Putanowicz, PhD  < address@hidden  >
> > > Institute for Computational Civil Engng (L-5)
> > > Dept. of Civil Engng, Cracow Univ. of Technology
> > > www.l5.pk.edu.pl, tel. +48 12 628 2569, fax 2034
> > >
> > > _______________________________________________
> > > Getfem-users mailing list
> > > address@hidden
> > > https://mail.gna.org/listinfo/getfem-users
> > >
>
> --
> Roman Putanowicz, PhD  < address@hidden  >
> Institute for Computational Civil Engng (L-5)
> Dept. of Civil Engng, Cracow Univ. of Technology
> www.l5.pk.edu.pl, tel. +48 12 628 2569, fax 2034
>
> _______________________________________________
> Getfem-users mailing list
> address@hidden
> https://mail.gna.org/listinfo/getfem-users