# Base.nullspace for general matrices
**URL:** https://discourse.julialang.org/t/base-nullspace-for-general-matrices/112356
**Category:** General Usage
**Created:** [March 31, 2024, 3:39pm UTC](https://discourse.julialang.org/t/base-nullspace-for-general-matrices/112356 "2024-03-31T15:39:58Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@azoviktor](https://discourse.julialang.org/u/azoviktor)
#### Post date: [March 31, 2024, 3:39pm UTC](https://discourse.julialang.org/t/base-nullspace-for-general-matrices/112356/1 "2024-03-31T15:39:58Z")
Let’s say I would like to use the `nullspace` method from julia Base module for a matrix of type `AbstractMatrix{MyNumberType}`. What interface should I implement in order to make it work? Does such an interface technically exist (since it is not documented)?
---
### Author:  [@mkitti](https://discourse.julialang.org/u/mkitti)
#### Post date: [March 31, 2024, 4:43pm UTC](https://discourse.julialang.org/t/base-nullspace-for-general-matrices/112356/2 "2024-03-31T16:43:28Z")
Looks like satisfying the asbtract array interface is sufficient. I’m not sure what kind of number you are dealing with though.
```julia-repl
julia> struct Foo{T} <: AbstractMatrix{T} end
julia> Base.getindex(::Foo{T}, _...) where T = zero(T)
julia> Base.size(::Foo) = (3,3)
julia> using LinearAlgebra
julia> nullspace(Foo{Int}())
3×3 Matrix{Float64}:
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0
```
[https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-array](https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-array)
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### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [March 31, 2024, 4:50pm UTC](https://discourse.julialang.org/t/base-nullspace-for-general-matrices/112356/3 "2024-03-31T16:50:46Z")
> [@azoviktor](#):
>
> Let’s say I would like to use the `nullspace` method from julia Base module for a matrix of type `AbstractMatrix{MyNumberType}`. What interface should I implement in order to make it work? Does such an interface technically exist (since it is not documented)?
`nullspace` uses the SVD, so you need a package like GenericLinearAlgebra.jl that supports SVD of your number type.
---
### Author:  [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)
#### Post date: [April 1, 2024, 10:33am UTC](https://discourse.julialang.org/t/base-nullspace-for-general-matrices/112356/4 "2024-04-01T10:33:54Z")
`GenericLinearAlgebra` despite its name is not really generic. It assumes your numbers are some kind of floating point objects. For example define a 51x51 Hilbert matrix
```julia
julia> m=[BigInt(1)//(n+m) for n in 1:51, m in 1:51];
julia> size(GenericLinearAlgebra.nullspace(m))
(51, 1)
```
while the matrix is invertible. I have written a few routines for really generic linear algebra (valid over any field, and some routines valid over any ring when applicable, similar to `det_bareiss`) which are in the package `GenLinearAlgebra`. These includes `nullspace`. I do not claim to have written the best possible algorithms, and I do not know if there has been other similar efforts. Note that the algorithms valid over any field are often not good ones for floating-point numbers.
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [April 1, 2024, 12:39pm UTC](https://discourse.julialang.org/t/base-nullspace-for-general-matrices/112356/5 "2024-04-01T12:39:29Z")
> [@Jean\_Michel](#):
>
> `GenericLinearAlgebra` despite its name is not really generic. It assumes your numbers are some kind of floating point objects.
The algorithms for exact arithmetic are _completely_ different from the algorithms for inexact arithmetic in many cases; GenericLinearAlgebra is geared towards the latter.
In inexact arithmetic, `nullspace` uses an SVD (which is inherently inexact due to the Abel–Ruffini theorem), with a cutoff for the singular values. In exact arithmetic, you’d compute a nullspace basis using elimination.
---
### Author:  [@Jean\_Michel](https://discourse.julialang.org/u/Jean_Michel)
#### Post date: [April 1, 2024, 1:24pm UTC](https://discourse.julialang.org/t/base-nullspace-for-general-matrices/112356/6 "2024-04-01T13:24:34Z")
Yes, that was my point. I do not know what is the best vocabulary to talk about this dichotomy:
exact/inexact, exact/approximate, complete field/general field ? You could possibly also do approximate computation with p-adic numbers.