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Math Help - Matrices- Transpose Help

  1. #1
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    Matrices- Transpose Help

    Prove the following:
    a) (A^T)^T=A
    b) (A + B)^T= A^T + B^T
    c)(AB)^T=(B^T)(A^T)
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  2. #2
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    Quote Originally Posted by amm345 View Post
    Prove the following:
    a) (A^T)^T=A
    b) (A + B)^T= A^T + B^T
    c)(AB)^T=(B^T)(A^T)
    I'll set you off on the first and then you should see how to do the rest.

    Use (i,j) notation: A = \sum a_{ij}.

    Then by definition: A^T = \sum a_{ji}.

    So, (A^T)^T = \left(\sum a_{ji}\right)^T = \sum a_{ij} = A .


    Hope this helps,
    pomp.
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