# Reduce error in non Hermitian matrix diagonalization

**URL:** https://discourse.julialang.org/t/reduce-error-in-non-hermitian-matrix-diagonalization/75877
**Category:** New to Julia
**Tags:** question, package, linearalgebra
**Created:** [February 5, 2022, 9:30pm UTC](https://discourse.julialang.org/t/reduce-error-in-non-hermitian-matrix-diagonalization/75877 "2022-02-05T21:30:20Z")
**Posts on this page:** 4
**Page:** 1

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### Author: ![jisutich](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jisutich/32/33342_2.png) [@jisutich](https://discourse.julialang.org/u/jisutich)
#### Post date: [February 5, 2022, 9:30pm UTC](https://discourse.julialang.org/t/reduce-error-in-non-hermitian-matrix-diagonalization/75877/1 "2022-02-05T21:30:20Z")

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Hi, guys:

I have limited knowledge about julia and other coding languages. Recently I am trying to diagonalize a series of matrices. Each matrix is obtained by some recursion relation and it is supposed to be Hermitian. But due to the round off error, I will get a non-Hermitian matrix. And this leads to an error in the diagonalized result. How to reduce the error as much as possible? I guess I can use Hermitian(A) or (A+A’)/2 to transfer this matrix to a Hermitian one at first. But I don’t know if this is a good idea.

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### Author: ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [February 5, 2022, 10:09pm UTC](https://discourse.julialang.org/t/reduce-error-in-non-hermitian-matrix-diagonalization/75877/2 "2022-02-05T22:09:12Z")

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If it’s just roundoff error, I would just use `Hermitian(A)`

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### Author: ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [February 5, 2022, 10:11pm UTC](https://discourse.julialang.org/t/reduce-error-in-non-hermitian-matrix-diagonalization/75877/3 "2022-02-05T22:11:01Z")

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See also [https://github.com/JuliaLang/julia/pull/31836](https://github.com/JuliaLang/julia/pull/31836)

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### Author: ![jisutich](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jisutich/32/33342_2.png) [@jisutich](https://discourse.julialang.org/u/jisutich)
#### Post date: [February 7, 2022, 2:40am UTC](https://discourse.julialang.org/t/reduce-error-in-non-hermitian-matrix-diagonalization/75877/4 "2022-02-07T02:40:35Z")

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Thanks！