A discussion about scale invariants for tensor functions

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