# Apply inverse of BigFloat sparse Hermitian matrix

**URL:** <https://discourse.julialang.org/t/apply-inverse-of-bigfloat-sparse-hermitian-matrix/123189>\
**Category:** New to Julia\
**Created:** [November 27, 2024, 10:52pm UTC](https://discourse.julialang.org/t/apply-inverse-of-bigfloat-sparse-hermitian-matrix/123189 "2024-11-27T22:52:18Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![EZ\_Money](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ez_money/32/213637_2.png) [@EZ\_Money](https://discourse.julialang.org/u/EZ_Money)\
**Post date:** [November 27, 2024, 10:52pm UTC](https://discourse.julialang.org/t/apply-inverse-of-bigfloat-sparse-hermitian-matrix/123189/1 "2024-11-27T22:52:18Z")

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Hi! I’m trying to find the smallest singular vector of a sparse (16900x16900) Hermitian BigFloat  
matrix A. Is there a standard way to do this?

My current idea is to use ArnoldiMethod.partialschur with a function that applies the inverse of A. To get this function, I would first find a sparse LU decomposition of A ( with IncompleteLU.jl, following [this guy](https://discourse.julialang.org/t/linsolve-on-sparsematrixcsc-bigfloat/60742/2) ), then apply one of the IterativeSolvers functions (like conjugate gradients??). Would that work?

(Another question is, if the original matrix has a 1d kernel, how can I find the kernel?)

I am not very familiar with how any of the linear algebra algorithms work (maybe I should learn), but I just want my eigenvector. Any help would be greatly appreciated! Thanks!

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<div class="post-metadata">

**Author:** ![EZ\_Money](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ez_money/32/213637_2.png) [@EZ\_Money](https://discourse.julialang.org/u/EZ_Money)\
**Post date:** [November 28, 2024, 8:40am UTC](https://discourse.julialang.org/t/apply-inverse-of-bigfloat-sparse-hermitian-matrix/123189/4 "2024-11-28T08:40:18Z")

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by the way are you ai? (out of curiosity) if not, sorry and thanks for answer!

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**Author:** ![dpo](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dpo/32/3335_2.png) [@dpo](https://discourse.julialang.org/u/dpo)\
**Post date:** [November 29, 2024, 3:07pm UTC](https://discourse.julialang.org/t/apply-inverse-of-bigfloat-sparse-hermitian-matrix/123189/6 "2024-11-29T15:07:41Z")

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Try Arpack.jl or TSVD.jl.