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Math Help - Transpose of Matrices

  1. #1
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    Transpose of Matrices

    Show that [AB]^t = B^t*A^t........ I know that this is true, I just need proof. I have attempted to figure it out, but I am only able to do it with concrete examples. can someone help me out. TIA!!!!
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  2. #2
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    Quote Originally Posted by TreeMoney View Post
    Show that [AB]^t = B^t*A^t........ I know that this is true, I just need proof. I have attempted to figure it out, but I am only able to do it with concrete examples. can someone help me out. TIA!!!!

    (B^tA^t)_{i,j}=\sum_k B^t_{i,k}A^t_{k,j}=\sum_k B_{k,i}A_{j,k} <br />
=\sum_k A_{j,k}B_{k,i}=(AB)_{j,i}=((AB)^t)_{i,j}<br />

    RonL
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