science forum Guru Wannabe
Joined: 03 May 2005
|Posted: Tue Jul 18, 2006 11:41 am Post subject:
# of independent tensor components
I have to solve simultaneous tensor equations like
[upper indices in front, lower behind the symbol]
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
Hauke Reddmann <:-EX8 email@example.com