The discussion revolves around the properties of Cartesian tensors, specifically focusing on the conditions under which a certain equation (I-10) equals 1 or 0 based on the indices involved. The scope includes theoretical aspects of tensor mechanics and mathematical reasoning related to tensor equations.
The discussion contains multiple viewpoints regarding the interpretation of the equations and the definitions of terms, indicating that there is no consensus on the understanding of the relationship between the indices and the equations presented.
Participants reference specific equations (I-9 and I-10) and their conditions without providing complete definitions or derivations, which may limit understanding of the context and assumptions involved.
Consider the case of ##x'_0=1, x'_1=0, x'_2=0##. In this case, only the terms with ##k=0## contribute to the sum in the eqn. I-9, which becomes ##x'_i=a_{ij}a_{0j}##. For ##i=0## it becomes ##1=a_{0j}a_{0j}##, for ##i=1## it becomes ##0=a_{1j}a_{0j}##, etc. For all combinations of ##k## and ##i##, you get the eqn. I-10.Worn_Out_Tools said:
No. ##i, j, k## are indices.Worn_Out_Tools said: