Tensors and Relativity: Assignment 3

Hints 3

Hints 3

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  • (1) Just use the results in section 3.2 of the notes.

     

  • (2a) A set of vectors tex2html_wrap_inline361 are linearly independent if and only if there exists no real numbers tex2html_wrap_inline363 such that

    eqnarray341

     

    (2b) Equation (3) in the assignment will give you four linear equations for the four components of tex2html_wrap_inline365 , which you should be able to solve very easily.

    (2c) Having got the components of tex2html_wrap_inline365 , it is easy to find the value of tex2html_wrap_inline369 .

    (2d) This problem is similar to part (2a).

     

  • (3) Assume that tex2html_wrap_inline371 and tex2html_wrap_inline373 . Then evaluate tex2html_wrap_inline375 and tex2html_wrap_inline377 . You should get different results.

     

  • (4a) Just use the definitions in section 3.3 and 3.4 of the lecture notes.

    (4b) Compare how tex2html_wrap_inline379 and tex2html_wrap_inline381 transform.

    (4c) No hint here!!

     

  • (5) Just use the definitions of symmetric and anti- symmetric tensors in section 3.3 of the notes and juggle the indices!

     

  • (6) A chocolate bar will go to the first person who presents me a perfect solution!!