I have what I think is a simultaneous eigenvalue problem in three parameters:
$$\alpha A_1x + \beta B_1x + \gamma C_1x + D_1x = 0$$ $$\alpha A_2x + \beta B_2x + \gamma C_2x + D_2x = 0$$ $$\alpha A_3x + \beta B_3x + \gamma C_3x + D_3x = 0$$
The matrices $A_1$,$B_1$ etc are square and may be singular. I want to solve for the vector x and the scalar parameters $\alpha$, $\beta$ and $\gamma$.
I think this is a simultaneous eigenvalue problem, but other articles seems to talk about a different $x$ for each equation, where I have a shared $x$.
Does anyone know how to solve this type of problem? Are there libraries available to solve simultaneous eigenvalue problems?