As the title says I have a large sparse matrix, 262000 by 262000, and i want to know how the number of times that an eigenvalue is degenerate. I can get the eigenvalue using the arnoldi method but after that i am clueless in what should i do. I can't calculate all of the eigenvalues of the matrix since i run out of memory.
If your memory is big enough to compute the orthogonal projector to the complement of each eigenvector and look for another eigenvalue of the same value in the projected matrix
A . e = \lambda e P = TensorProduct[e, Transpose@Conjugate@e] (1-P) e = 0 Solve[ (1-P).A.(1-P) . x == lambda x,x]