# Eigen produces non-normalized eigenvectors

**URL:** <https://discourse.julialang.org/t/eigen-produces-non-normalized-eigenvectors/129829>\
**Category:** Numerics\
**Created:** [June 12, 2025, 10:52am UTC](https://discourse.julialang.org/t/eigen-produces-non-normalized-eigenvectors/129829 "2025-06-12T10:52:42Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![abraemer](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/abraemer/32/51403_2.png) [@abraemer](https://discourse.julialang.org/u/abraemer)\
**Post date:** [June 12, 2025, 11:09am UTC](https://discourse.julialang.org/t/eigen-produces-non-normalized-eigenvectors/129829/2 "2025-06-12T11:09:20Z")

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Usually the eigen vectors are indeed normalized (at least for regular eigenvalue problem). Can you give a simple example where this is not the case?

Recently, there was a longer thread where some numerical instability caused weird results in `eigen`. Maybe your issue is related?

> [@Eigen fails to find eigenvectors](https://discourse.julialang.org/t/eigen-fails-to-find-eigenvectors/129072):
>
> I am confused. I’m finding the eigenvalues and eigenvectors of a 3x3 matrix, but it seems like eigen does not find all the vectors correctly. julia\> using LinearAlgebra julia\> A = [1 1 1; 1 1 1; -1 -1 -1] 3×3 Matrix{Int64}: 1 1 1 1 1 1 -1 -1 -1 julia\> D, Q = eigen(A) Eigen{Float64, Float64, Matrix{Float64}, Vector{Float64}} values: 3-element Vector{Float64}: 0.0 9.860761315262648e-32 0.9999999999999996 vectors: 3×3 Matrix{Float64}: -2.21943e-17 -3.20494e-16 0.57735 0.7…

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