I Summation convention with expressions containing parentheses

[emq]

Is (T_ii)² equivalent to (∑_{i = 1}ⁿT_ii)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.

 

[hilbert2]

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]

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 $a_i b_i c_i = a_1 b_1 c_1 + a_2 b_2 c_2 + a_3 b_3 c_3$.

Yes, that's certainly true, I revised my question for the sake of clarity.

 

[PeroK]

Is (T_ii)² equivalent to (∑_{i = 1}ⁿT_ii)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.

Logically, that makes sense. In general, you interpret what is in the brackets first.