The discussion revolves around the interpretation of expressions involving Einstein summation convention, particularly focusing on whether operations indicated by parentheses should be applied before or after performing the summation. Participants explore the implications of this interpretation in the context of tensor notation and mathematical rules.
Participants express differing views on the interpretation of the summation convention and the application of mathematical operations, indicating that multiple competing views remain without a consensus.
There are limitations regarding the clarity of rules around the summation convention and the use of indices in tensor notation, which remain unresolved in the discussion.
hilbert2 said:At least in the tensor-related textbook I've been reading most recently, it is said that the same index should not be repeated more than twice in any expression. For instance, if ##\mathbf{a},\mathbf{b}## and ##\mathbf{c}## are three-component vectors, you shouldn't use the shorthand notation ##a_i b_i c_i = a_1 b_1 c_1 + a_2 b_2 c_2 + a_3 b_3 c_3##.
emq said:Is (Tii)2 equivalent to (∑i = 1nTii)2? That is, when you encounter parentheses with Einstein summation, you perform the summation first and then apply any mathematical operations indicated by the parentheses? The solutions manual gives a solution to a problem I've been working out seems to indicate this is the case, but I haven't seen it stated as a rule.