The discussion centers on the behavior of Cartesian tensors, specifically addressing why equation I-10 equals 1 when k equals i and 0 when k does not equal i. The contributors clarify that in the case where ##x'_0=1, x'_1=0, x'_2=0##, only terms with ##k=0## contribute to the sum in equation I-9, leading to the conclusion that for ##i=0##, the equation simplifies to ##1=a_{0j}a_{0j}##. The shorthand notation “a” refers to the cosine function, but the indices ##i, j, k## are not functions but rather indices that denote specific components in the tensor notation.
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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: