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 Exercise [13.40] 
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Joined: 13 Jul 2010, 19:22
Posts: 2
Post Exercise [13.40]
Part 1

Suppose\{e^i\} is a basis forV^*, then \{e^i \tensor e^j \} is a basis for V^* \tensor V^*. All symmetric tensors in V^* \tensor V^* could be written as \a_{ij}e^i \tensor e^j, where a_{ij} = a{ji}, there are totally n(n-1)/2 +n = n(n+1)/2 such symmetric tensors.

A symmetric tensor could be naturally identify with a symmetric matrix

[a^1_1, a^1_2, a^1_3 ...]<br />[a^1_2, a^2_2, a^2_3 ...]<br />[a^1_3, a^2_3, a^3_3 ...]


23 Jul 2010, 23:43

Joined: 13 Jul 2010, 19:22
Posts: 2
Post Re: Exercise [13.40]
Please delete the above message. Seems like the tex is not working, or I am doing something wrong.


23 Jul 2010, 23:45
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Joined: 07 Jun 2008, 08:21
Posts: 235
Post Re: Exercise [13.40]
tex is not working. Create a pdf file and attach that to your post instead


24 Jul 2010, 08:39
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