# Eigen solution of Matrix{Rational{BigInt}}

**URL:** <https://discourse.julialang.org/t/eigen-solution-of-matrix-rational-bigint/19627>\
**Category:** General Usage\
**Created:** [January 14, 2019, 4:58pm UTC](https://discourse.julialang.org/t/eigen-solution-of-matrix-rational-bigint/19627 "2019-01-14T16:58:11Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![fgerick](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fgerick/32/13228_2.png) [@fgerick](https://discourse.julialang.org/u/fgerick)\
**Post date:** [January 14, 2019, 4:58pm UTC](https://discourse.julialang.org/t/eigen-solution-of-matrix-rational-bigint/19627/1 "2019-01-14T16:58:11Z")

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Is there already a way to get eigenvalues and eigenvectors with BigInt/BigFloat accuracy? I know about the [GenericLinearAlgebra.jl](https://github.com/JuliaLinearAlgebra/GenericLinearAlgebra.jl) implementation for `eigvals`, but I need the high accuracy in the eigenvectors. Anybody knows about an implementation already out there? If not, what could be the easiest way to get a working code (I don’t care too much about speed as long as its faster than symbolic math tools like SymPy or Mathematica) ?

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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:** [January 14, 2019, 6:32pm UTC](https://discourse.julialang.org/t/eigen-solution-of-matrix-rational-bigint/19627/2 "2019-01-14T18:32:56Z")

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Do you need all of the eigenvalues and eigenvectors, or just particular ones? Is your matrix arbitrary, or special in some way (real-symmetric, tridiagonal, etcetera)?

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**Author:** ![fgerick](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fgerick/32/13228_2.png) [@fgerick](https://discourse.julialang.org/u/fgerick)\
**Post date:** [January 14, 2019, 6:44pm UTC](https://discourse.julialang.org/t/eigen-solution-of-matrix-rational-bigint/19627/3 "2019-01-14T18:44:55Z")

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I have arbitrary real matrices. Actually I need to solve a generalized problem, but in my case the matrix is invertable to make it a standard problem. I’d be happy about both a targeted and a dense solver, no real preference.

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**Author:** ![andreasnoack](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andreasnoack/32/27_2.png) [@andreasnoack](https://discourse.julialang.org/u/andreasnoack)\
**Post date:** [January 14, 2019, 6:51pm UTC](https://discourse.julialang.org/t/eigen-solution-of-matrix-rational-bigint/19627/4 "2019-01-14T18:51:06Z")

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Take a look at [GitHub - RalphAS/GenericSchur.jl: Julia package for Schur decomposition of matrices with generic element types](https://github.com/RalphAS/GenericSchur.jl). To get the eigenvectors, you’d have to convert the input matrix to complex before computing the Schur factorization.

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**Author:** ![fgerick](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fgerick/32/13228_2.png) [@fgerick](https://discourse.julialang.org/u/fgerick)\
**Post date:** [January 14, 2019, 9:56pm UTC](https://discourse.julialang.org/t/eigen-solution-of-matrix-rational-bigint/19627/5 "2019-01-14T21:56:18Z")

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Thanks. That’s basically what i needed.