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Math Help - Euclidean inner product

  1. #1
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    Euclidean inner product

    Question 1
    In each part, use the given inner product on \mathbb{R}^{2} to find ||w||, where w = (-1,3).
    (a) the Euclidean inner product
    (b) the weighted Euclidean inner product <u,v> = 3u1v1 + 2u2v2, where u = (u1,u2) and v = (v1,v2)
    (c) the inner product generated by the matrix \begin{bmatrix} 1 & 2 \\ -1 & 3 \end{bmatrix}


    Question 2
    Show that <u,v> = 5u1v1 - u1v2 -u2v1 + 10u2v2 is the inner product on \mathbb{R}^{2} generated by  A = \begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix}

    Attempt:
    \begin{bmatrix} v_{1} & v_{2} \end{bmatrix} \begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix} \begin{bmatrix} 2 & 1 \\ -1 & 3 \end{bmatrix}\begin{bmatrix} u_{1} \\u_{2} \end{bmatrix}

    but i couldn't get the equation above. I suppose that the above formula only hold for diagonal matrix?
    Last edited by whyyie; June 7th 2012 at 01:36 AM.
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  2. #2
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    Re: Euclidean inner product

    instead of using AA, use ATA, so you get a symmetric matrix.
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