# Large Sparse Hermitian Matrix - Intermediate Eigenvalue Problem

**URL:** <https://discourse.julialang.org/t/large-sparse-hermitian-matrix-intermediate-eigenvalue-problem/131600>\
**Category:** General Usage\
**Tags:** linearalgebra, sparse, arpack, solver\
**Created:** [August 14, 2025, 10:09am UTC](https://discourse.julialang.org/t/large-sparse-hermitian-matrix-intermediate-eigenvalue-problem/131600 "2025-08-14T10:09:33Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![RayleighLord](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rayleighlord/32/33592_2.png) [@RayleighLord](https://discourse.julialang.org/u/RayleighLord)\
**Post date:** [August 14, 2025, 10:54am UTC](https://discourse.julialang.org/t/large-sparse-hermitian-matrix-intermediate-eigenvalue-problem/131600/2 "2025-08-14T10:54:48Z")

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Is it possible for you to share the matrix? I think one of the most efficient ways would be to compute the action of the inverse of the shifted matrix (A-\sigma I)^{-1} on a vector x, rather than including the entire matrix inside a `LinearMap` (this is explained in this [post](https://discourse.julialang.org/t/smallest-magnitude-eigenvalues-of-the-generalized-eigenvalue-equation-for-a-large-sparse-matrix/75485/11)),

If you can share the matrix, I can try to give you an example for this case since I have been doing something similar these past weeks.

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