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| e123 | = 0 if any of i, j, k are equal = 1 if i,j, k are unequal and in cyclic order = -1 if i,j, k are unequal and not in cyclic order |
This can be defined by a determinant
| e123= |
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This represents the cross product:
c = a × b
or in tensor notation:
ci = eijk a j b k
then expanding out gives:
c1 = e123 a 2 b 3 + e132 a 3 b 2 = a 2 b 3 - a 3 b 2
c2 = e231 a 3 b 1 + e213 a 1 b 3 = a 3 b 1 - a 1 b 3
c3 = e312 a 1 b 2 + e321 a 2 b 1 = a 1 b 2 - a 2 b 1
There are certain quantities, operators and concepts that seem to come in pairs:
This page investigates this.
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Book Shop - Further reading. Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them. |
       Tensor Analysis. |
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Commercial Software Shop Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them. |
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Can you help? Please send me any improvements to here. I would appreciate ideas to make the pages more useful including error correction, ideas for new pages, improvements to wording. It helps if you quote the full URL of the page. |
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Terminology and Notation Specific to this page here: |
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program I am working on a project which uses these principles, if you would like to help me with this you are welcome to join in, here: |
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Copyright (c) 1998-2008 Martin John Baker - All rights reserved.
