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 <[email protected]> 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 <[email protected]>
>>
>> > 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 < [email protected] >
>> > 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
>> > [email protected]
>> > https://mail.gna.org/listinfo/getfem-users
>> >
>
> --
> Roman Putanowicz, PhD < [email protected] >
> 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
> [email protected]
> https://mail.gna.org/listinfo/getfem-users
>
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