CircleTimes - tensor product operator

CircleTimes[t1, t2, ..., tn]
allows one to calculate the tensor product of given tensors.
  • t1, t2, ..., tn - tensors.
  • The main syntax is as follows: T or CircleTimes[, T] where and T are tensors.
  • To calculate tensor product for tensors 1, 2, ..k use the following CircleTimes[1, 2, ...k] or 1 2..k
  • Tensor product is linear operation with respect to its arguments. Thus if , are 0-forms then: (1)(2+3)=(1)(2)+(1)(3)
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Declare Vectors:
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Declare tensors:
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Using CircleTimes- procedure: Tensor product is linear operation with respect to its arguments:
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Some more examples:
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And with Lie derivative ( is 1-form see Tensors defenition above):
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And again:
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And finally:
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