Quadratic Eigenvalue problem/block formation

I’m trying to solve a quadratic eigenvalue problem:
[tex]\lambda^2 M + \lambda C + K =0[/tex] where the three matrices are defined in the program as bilinear forms.

Normally this problem is solved by solving the larger eigenvalue problem as seen on Wikipedia Quadratic Eigenvalue Problem

The issue is that bilinear forms, as far as I’m aware, cannot be placed into a block matrix form. Has anyone dealt with this issue or has a method to allow for the solving of the quadratic problem given the bilinear forms?