The discussion centers on the interpretation of expressions involving Einstein summation notation, specifically whether (Tii)² is equivalent to (∑i=1n Tii)². Participants confirm that the summation should be performed first, followed by any operations indicated by parentheses. Additionally, it is emphasized that the same index should not be repeated more than twice in expressions, as stated in tensor-related textbooks. This guideline is crucial for maintaining clarity in tensor calculations.
PREREQUISITESStudents and professionals in mathematics, physics, and engineering who are working with tensor analysis and require a clear understanding of Einstein summation notation and its rules.
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.