# Smallest magnitude eigenvalues of the generalized eigenvalue equation for a large sparse matrix

**URL:** <https://discourse.julialang.org/t/smallest-magnitude-eigenvalues-of-the-generalized-eigenvalue-equation-for-a-large-sparse-matrix/75485>\
**Category:** General Usage\
**Tags:** question, eigenvalue, arpack\
**Created:** [January 31, 2022, 2:24am UTC](https://discourse.julialang.org/t/smallest-magnitude-eigenvalues-of-the-generalized-eigenvalue-equation-for-a-large-sparse-matrix/75485 "2022-01-31T02:24:07Z")\
**Posts on this page:** 1\
**Page:** 2

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**Author:** ![lmiq](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/lmiq/32/18314_2.png) [@lmiq](https://discourse.julialang.org/u/lmiq)\
**Post date:** [February 2, 2022, 12:05pm UTC](https://discourse.julialang.org/t/smallest-magnitude-eigenvalues-of-the-generalized-eigenvalue-equation-for-a-large-sparse-matrix/75485/22 "2022-02-02T12:05:42Z")

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> [@antoine-levitt](#):
>
> That assumes the density matrix is sparse (like linear scaling DFT methods), right?

Yes, exactly, we were implementing that for large molecular systems (not solids), and the idea is to preserve the sparsity all the time.

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