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# of independent tensor components
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Hauke Reddmann
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Joined: 03 May 2005
Posts: 112

PostPosted: Tue Jul 18, 2006 11:41 am    Post subject: # of independent tensor components Reply with quote

I have to solve simultaneous tensor equations like
[upper indices in front, lower behind the symbol]

abPcd*Qec=eaOdf*Qfb
abPcd*Qcd=w*Qab (w scalar)
....
etc., including some Einstein summation.

Evidently I want to choose a "coordinate system"
where as many components vanish as possible.
One possible transformation is multiplying with
a'Ta for each index a, even if dummy (i.e
Qec=Q'e'c'*e'Te*c'Tc etc.) - as long as
xTy*yTz=Kronecker(x,z) all T will vanish in a
puff of index smoke and the equation in O,P,Q
still looks exactly the same.

But I don't know whether I can get rid of even
more components. E.g. assume I want to pepper
Q with zeroes and Q has 2 numbers for each
index, which of Q11,Q12,Q21,Q22 can be set to
zero WLOG?
--
Hauke Reddmann <:-EX8 fc3a501@uni-hamburg.de
His-Ala-Sec-Lys-Glu Arg-Glu-Asp-Asp-Met-Ala-Asn-Asn
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