The variational formulation for (5) can be written in the following matrix form :
or
where A is 
and M is ( u, v ).
These are familiar to us as the generalized eigenvalue problem
, with
the generalized eigenvalues.
Using MATLAB, the square roots of the generalized eigenvalues have been calculated for the following discretizations of our L-shaped domain :
The variational formulation for (7) can be written in the following matrix form :
where 
.
Numerical experiments involved writting the above matrix formulation in the following
manner : 
.
Setting the k on the outside of the parantheses to be lambda,
, we fix k and
solve the associated generalized eigenvalue problem.
Another experiment involved running through all k values that were a
problem for (5),
building the matrix 
and
finding the determinant.
Determinant calculations for :