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Thread: Simple question about algebra y^T X y

  1. #1
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    Simple question about algebra y^T X y

    Hey can anybody explain to me why the function

    $\displaystyle
    f(X,y) = y^T X y
    $

    is linear in $\displaystyle X$ for each $\displaystyle y$, where $\displaystyle X \in R^{n \times n}$ is a symmetric matrix, and $\displaystyle y \in R^n$ is a vector.
    Last edited by mr fantastic; Nov 21st 2010 at 01:24 PM. Reason: Restored deleted question.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    We have:

    1.- $\displaystyle f(X_1+X_2,y)=y^t(X_1+X_2)y=y^t(X_1y+X_2y)=\ldots$

    2.- $\displaystyle f(\lambda X,y)=y^t(\lambda X)y=\ldots$

    Could you continue?

    Regards.

    Fernando Revilla
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