Solve the following nonlinear equations for $v$ and $w$
where $\lambda_1, \lambda_2, \lambda_3$ are real. $A$ is a symmetric matrix.
How would you generalize to the case
Where both A and B are symmetric? Would it help if they are also similar and each of them has exactly $n/2$ eigenvalues equal to $+1$ and $n/2$ eigenvalues equal to $-1$?