# How can i know the number of times that an eigenvalue is degenerate for a large matrix?

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.

• Use Tally on the resulting list of eigenvalues? Since they are numerical, you may want to Round them to an appropriate precision first, to ease the comparison. Commented May 23, 2023 at 17:00
• The problem is: i can't calculate all of them without running out of memory. Commented May 23, 2023 at 17:03
• Oh ok, I thought that was obvious since i said that was a large matrix. Commented May 23, 2023 at 17:22
• provide minimal real example. just reduce your matrix and insert ur question. and what u tried with Large matrix that lead you to memory problem! Commented May 23, 2023 at 17:29

   A . e = \lambda e