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Math Help - Prove the following identity

  1. #1
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    Prove the following identity

    Show that for A \in M_n(\mathbb{R}) and x,y \in \mathbb{R}^n

    x \cdot Ay = y \cdot Ax

    I get
    y \cdot Ax = y^t Ax but i cannot see where to go now

    I think it may involve (AB)^t=B^tA^t
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Prove the following identity

    Hi FGT12!

    You're on the right track.
    Can you say what (y^tAx)^t is?
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  3. #3
    MHF Contributor
    Opalg's Avatar
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    Re: Prove the following identity

    Quote Originally Posted by FGT12 View Post
    Show that for A \in M_n(\mathbb{R}) and x,y \in \mathbb{R}^n

    x \cdot Ay = y \cdot Ax

    I get
    y \cdot Ax = y^t Ax but i cannot see where to go now

    I think it may involve (AB)^t=B^tA^t
    There is a missing {\color{white}.}^t somewhere. It should be x \cdot A^ty = y \cdot Ax. Either that, or there is a missing condition A^t=A.
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