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February 23, 2007, 15:28
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Einstein's summation convention
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#1 |
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Guest
Posts: n/a
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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 |
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February 23, 2007, 16:09
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Re: Einstein's summation convention
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#2 |
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Guest
Posts: n/a
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Its correct. Just work out a case of 2x2 matrices to convince yourself.
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February 23, 2007, 16:28
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Re: Einstein's summation convention
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#3 |
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Guest
Posts: n/a
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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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