(1) Fi = mai (where i = subscript)
(2) F'i = ma'i (where ' denotes a change in coordinate system)
(13) Tqr = lqi*lrj*T'ij (where T = stress tensor and q,r,i,j are subscripts
Calculations:
Components of Fi and F'i are the projections of F on the fixed mutually perpendicular unit vectors e^(i) and e^(i)', respectively, and are thus only different notationally. (2) holds iff (1) holds
...