4 comments on “Tensor Algebra Part 2

  1. ADEYEYE O.J. says:

    well simplified

  2. George Oladayo says:

    Good morning sir,

    Is the vector space closed under cross product?
    Is the vector space closed under tensor product?
    Is the vector space closed under vector cross?

    • oafak says:

      The ONLY operation requiring closure for a vector space is ADDITION. The vector space is actually closed under cross product but that is NOT a requirement for a set to be a vector space. The reason is that cross product is defined under restrictive conditions: That the space is Euclidean and three dimensional.These are not essential for a set to be a vector space.
      Of course the result of the tensor product is NOT the same as the arguments of the operation! Two vectors create a tensor. Consequently, there is no closure there.
      The vector cross is not an operation. It is the definition of a particular tensor. The idea of closure in this circumstance is irrelevant.
      In summary, when we are discussing closure for a vector space, we are only talking about addition – not any other operation.

  3. Abdul-Hammid says:

    Sir, i noticed that you have not uploaded the updated version of the last slide (Tensor Algebra Part 2)

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