$f$ is an unknown column vector and $A,B$ are square matrices. Let $x_1 = f^TBf$ and $x_2=f^TA^TBAf$.
Is there a way to estimate somehow $x_1$ given $x_2$, $A$ and $B$?
Will it be possible if a large number of such $x^j_1,x^j_2$ were available, where $j$ denotes the index and each such pair corresponds to a different and known $B_j$?
Edit: A is invertible (or at least has a pseudo inverse).
Thanks.