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- Path: sparky!uunet!portal!lll-winken!sol.ctr.columbia.edu!destroyer!gatech!rutgers!ub!acsu.buffalo.edu!adumi-v
- From: adumi-v@acsu.buffalo.edu (virgil adumitroaie)
- Newsgroups: sci.math
- Subject: Hint?
- Message-ID: <Bvtw1A.3y3@acsu.buffalo.edu>
- Date: 9 Oct 92 00:29:34 GMT
- Sender: nntp@acsu.buffalo.edu
- Organization: UB
- Lines: 41
- Originator: adumi-v@cfd11.eng.buffalo.edu
- Nntp-Posting-Host: cfd11.eng.buffalo.edu
-
-
-
-
-
- I wonder if somebody could give me a hand in solving
- an easy problem, which I did it once some time ago, but it
- seems that it doesn't work anymore (and I threw away the
- scratch notes).
-
- The problem is to demonstrate the tensorial relation
-
- E E = d d - d d
- ijk pqk ip jq iq jp
-
- where E is the alternating tensor and d the Kronecker tensor.
-
- The way I did it once was using the representation of
-
- | d d d |
- ^ ^ ^ | ii ij ik|
- E as E =e .(e x e )=| d d d |
- ijk i j k | ji jj jk|
- | d d d |
- | ki kj kk|
- ^
- where e are the orthogonal unit vectors. The same thing for
- i
-
- E , and then multiplying the two matrices I got the desired
- pqk
-
- relation, but now I get a mess. If you have seen this idea of
-
- demonstration anywhere else, or you can solve in this way, please
-
- give me a hint.
-
-
- Thanks,
-
- Virgil
-