# Einstein's summation convention

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 February 23, 2007, 15:28 Einstein's summation convention #1 Lionel S. Guest   Posts: n/a Hi all, I found a strange consistency leak in summation convections: Suppose I have two matrix, A and B tr(AB) = (AB)_ii Since (AB)_ij = A_im B_mj Then tr(AB) = A_im B_mi But if A is symmetric it means that tr(AB) = A_mi B_mi Which is equal to A:B, the scalar (inner) tensorial product. Which is impossible because tr(AB) not equal to A:B even A or B are symmetric There is a fault somewhere, but I can't find it. Do you have an idea ? Thanx in advance... Bye Lionel

 February 23, 2007, 16:09 Re: Einstein's summation convention #2 Praveen. C Guest   Posts: n/a Its correct. Just work out a case of 2x2 matrices to convince yourself.

 February 23, 2007, 16:28 Re: Einstein's summation convention #3 Lionel S. Guest   Posts: n/a Yes ... surprisingly, it works, I didn't believe it first. ... Thanx, it could help for one of my next exams (mechanics of composite materials) ;-)

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