1. If CabAa Bb is a scalar for two arbitrary vectors Aa and Bb show that Cab is a tensor.
2. If the 4-vectors Ua=Gamma(u) (c,u) and Va=Gamma(v)
(c,v) are the 4-vectors
velocity of two particles in some frame of reference, show that UaVa=Gamma(w)c2
where w is the relative velocity of the two particles as viewed in the
rest frame of one particle or the other. Hint: Evaluate the expression
first in the rest frame of one particle, and then generalize.