Summation convention with expressions containing parentheses

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emq
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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.
 
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hilbert2
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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##.
 
  • #3
emq
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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.
 
  • #4
PeroK
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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.
Logically, that makes sense. In general, you interpret what is in the brackets first.
 

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