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Thread: Quadratic Forms - Reduction Techniques

  1. #1
    Junior Member ibnashraf's Avatar
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    Quadratic Forms - Reduction Techniques

    hi all,

    i am trying to do an assignment here and i would like to verify my answer to the following question:

    Let $\displaystyle Q=x_1^2+2x_2^2-7x_3^2-4x_1x_2+8x_1x_3$
    Find a non-singular matrix $\displaystyle P$ and a diagonal matrix $\displaystyle D=diag(d_1,d_2,d_3)$ such that Q is transformed to $\displaystyle Q'=d_1y_1^2+d_2y_2^2+d_3y_3^2$; under the transformation $\displaystyle X=PY$
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  2. #2
    Junior Member ibnashraf's Avatar
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    Re: Quadratic Forms - Reduction Techniques

    i used the congruence method of reduction and i ended up with

    $\displaystyle D=diag(1, 4, -288)$

    and $\displaystyle P=\left(\begin{array}{ccc}1&0&-8\\0&4&28\\0&2&16\end{array}\right)$

    Is my answer correct?
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