I understand that the quadratic form, $f(x) = x^TAx$, is convex with respect to $x$ so long as the matrix $A$ is positive semi-definite.
If we assume that $A$ remains positive semi-definite, is the more general expression:
$f(\theta) = x^T(\theta)Ax(\theta)$
also convex with respect to the parameters $\theta$?
Is the answer an obvious yes or is there more to this that I am missing?