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Math Help - Matrix Proof

  1. #1
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    Matrix Proof

    Hey, I've been trying to prove that the inverse of the transpose of a matrix, is equal to the transpose of the inverse of a matrix, i.e.

    (A^T)^(-1)=(A^(-1))^T

    (also, some help on how to use TEX would be useful...)
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  2. #2
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    Re: Matrix Proof

    Are you allowed to assume that (AB)^{T}=B^{T}A^{T} ?

    If so, take the transpose of AA^{-1}=I and postmultiply by (A^{T})^{-1}.

    For the LaTex input, use the Go Advanced option and 'press' the \Sigma button and between the two [Tex] brackets type the line in as

    (A^{T})^{(-1)}=(A^{(-1)})^{T}.

    The ^ symbol translates as 'to the power of', and the power is then closed within the curley brackets.
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  3. #3
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    Re: Matrix Proof

    by definition an inverse for an nxn matrix A is an nxn matrix B such that AB = I.

    and....

    A^T(A^{-1})^T = (A^{-1}A)^T = I^T = I
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