Simple question about algebra y^T X y

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November 17th 2010, 10:15 AM
leoemil

Simple question about algebra y^T X y

Hey can anybody explain to me why the function

$<br /> f(X,y) = y^T X y<br />$

is linear in $X$ for each $y$ , where $X \in R^{n \times n}$ is a symmetric matrix, and $y \in R^n$ is a vector.
November 17th 2010, 01:22 PM
FernandoRevilla

We have:

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

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

Could you continue?

Regards.

Fernando Revilla

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