# Math Help - Simple question about algebra y^T X y

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

Hey can anybody explain to me why the function

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

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.

2. 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