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[Sponsors] |
June 7, 2005, 21:13 |
tensor terms
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#1 |
Guest
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is the term (in tensor notation)
A_i_j B_j_k S_k_i equivalent to : ( A_i_1 B_1_k + A_i_2 B_2_k + A_i_3 B_3_k ) S_k_i or if not can someone shed some light how to calculate the above mentioned terms |
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June 8, 2005, 03:05 |
Re: tensor terms
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#2 |
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There will be 27 terms in all since each of i, j, k are repeated and each index will take values 1,2,3. For every selection of two of the indices let the third index cycle through all its 3 values. For instance you could fix i and j and let k vary and then repeat the procedure for all 9 choices for i and j.
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June 8, 2005, 03:50 |
Re: tensor terms
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#3 |
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It is equal to the following triple sum, where each summation is over the entire range of the index value
∑<sub>i</sub> ∑<sub>j</sub> ∑<sub>k</sub>A<sub>ij</sub> B<sub>jk</sub> S<sub>ki</sub> If the indices vary over 1,2,3 then there are 27 terms in the above sum. The resultant is a scalar quantity. |
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June 8, 2005, 04:15 |
Re: tensor terms
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#4 |
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thanks people, if it will have 27 quantities then i have calculated it right, wanted to check with others, thanks again.
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