# \#eigenvalue

**URL:** https://discourse.julialang.org/tag/eigenvalue/939.md

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## [Smallest magnitude eigenvalues of the generalized eigenvalue equation for a large sparse matrix](https://discourse.julialang.org/t/smallest-magnitude-eigenvalues-of-the-generalized-eigenvalue-equation-for-a-large-sparse-matrix/75485)

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**Author:** [@Chong\_Wang](https://discourse.julialang.org/u/Chong_Wang)\
**Replies:** 20\
**Last updated:** [February 2, 2022, 12:05pm UTC](https://discourse.julialang.org/t/smallest-magnitude-eigenvalues-of-the-generalized-eigenvalue-equation-for-a-large-sparse-matrix/75485 "2022-02-02T12:05:42Z")

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I have a generalized eigenvalue problem Hx=\\lambda S x to solve, where H is Hermitian and S is positive definite. Both H and S are sparse matrices and their dimensions (size(H, 1)) are on the order of 10^5. Roughly 1% of…