A discussion about scale invariants for tensor functions

It is found that in some cases the complete and irreducible scale invariant s given by Ref.[1] are not independent. There are some implicit functional relations among them. The scale invariants for two different cases are calc ulated. The first case is an arbitrary second order tensor. The second case includes a symmetric tensor, an antisymmetric tensor and a vector. By usin g the eigentensor notation it is proved that in the first case there are on ly six independent scale invariants rather than seven as reported in Ref.[1 ] and in the second case there are only nine independent scale invariants w hich are less than that obtained in Ref.[1].