Invariants of a second-order tensor T

The following three scalars remain independent of the choice of coordinate system in which the components of T are defined and hence are caUed the invariants of tensor T  

262 APPENDIX - SUMMARY OF VECTOR AND TENSOR ANALYSIS The second invariant is the trace of T i.e. T.T, found as II = trace of = tr T jTp 

It can hence be seen that the magnitude of a symmetric tensor S is related to its second invariant as 

---