# Is there a \\ operator for Unitful?
**URL:** https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195
**Category:** New to Julia
**Tags:** linearalgebra, unitful, sympy
**Created:** [December 27, 2022, 7:19pm UTC](https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195 "2022-12-27T19:19:05Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@FelixHeox](https://discourse.julialang.org/u/FelixHeox)
#### Post date: [December 27, 2022, 7:19pm UTC](https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195/1 "2022-12-27T19:19:05Z")
I was running into a problem using the \ (linear system solver) operator in Julia. I guess I wrongly assumed the \ operator was overloaded for matrices/vectors with entries of type \<: Number (witch unitful types are). Is there any way to easily overload the \ operator to accept unitful types, or perhaps a different operator/function that works for all types that are subtypes of Number (since I plan on using Sym and Float/Integer types in my code as well)
Environment: Pluto on MacOS
Packages: Unitful, Sympy, Plots, PlutoUI
Code:
```julia
let
a11 = 1u"m"
a12 = 2u"ft"
a21 = 5u"mm"
a22 = 0u"inch"
A = [a11 a12; a21 a22]
b = [3u"inch"; 1u"mm"]
x = A \ b # This line throws error
end
```
Error:
`MethodError: no method matching (Unitful.Quantity{Rational{Int64}})(::Rational{Int64})`
---
### Author:  [@heliosdrm](https://discourse.julialang.org/u/heliosdrm)
#### Post date: [December 27, 2022, 7:33pm UTC](https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195/2 "2022-12-27T19:33:02Z")
I don’t think there is an easy way to define a unique, unambiguous solution to that example problem. Which should the units of the elements of `x`? Moreover, in this case it’s only a matter of scale between units of the same kind, but for arbitrary units in `A` and `b`, it might be impossible to solve.
---
### Author:  [@Dan](https://discourse.julialang.org/u/Dan)
#### Post date: [December 27, 2022, 7:54pm UTC](https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195/3 "2022-12-27T19:54:20Z")
Maybe something along these lines:
```julia
using LinearAlgebra, Unitful
import LinearAlgebra: \
(\)(A::Matrix{Quantity{T,U,V}}, B::AbstractVecOrMat) where {T,U,V} =
Quantity.(ustrip(A)\ustrip(B), unit(eltype(B))/unit(eltype(A)))
```
With this definition:
```julia
julia> A\b
2-element Vector{Rational{Int64}}:
1//5
-619//3048
julia> c = ustrip(b)
2-element reinterpret(Rational{Int64}...):
381//5000
1//1000
julia> A\c
2-element Vector{Quantity{Rational{Int64}...}}:
1//5 m^-1
-619//3048 m^-1
```
But this was a quick sketch, might be ins-and-outs to fix yet.
---
### Author:  [@FelixHeox](https://discourse.julialang.org/u/FelixHeox)
#### Post date: [December 27, 2022, 8:58pm UTC](https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195/4 "2022-12-27T20:58:26Z")
Oh yeah, it makes sense that the ‘b’ vector would be in units of Length\*mysteryunit since Ax = b, and x is unknown. Maybe x can be solved given the units of b?
---
### Author:  [@giordano](https://discourse.julialang.org/u/giordano)
#### Post date: [December 27, 2022, 11:18pm UTC](https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195/5 "2022-12-27T23:18:49Z")
Using the one-argument [`ustrip`](https://painterqubits.github.io/Unitful.jl/stable/manipulations/#Unitful.ustrip) method is generally a bad idea: you don’t know what you’re stripping, it works well only for the trivial case where you have all homogeneous quantities.
---
### Author:  [@FelixHeox](https://discourse.julialang.org/u/FelixHeox)
#### Post date: [December 27, 2022, 11:56pm UTC](https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195/6 "2022-12-27T23:56:20Z")
Thanks for the advice! I changed up the method a little bit to ensure that all unit of elements in the matrices A and B are the same before using the system solver.
```julia
function Base.:\(A::Matrix{Quantity{T,U,V}}, B::AbstractVecOrMat) where {T,U,V}
if typeof(unit(eltype(A))) ≠ Unitful.FreeUnits{(), NoDims, nothing}
A = map(x -> uconvert(unit(eltype(A)), x), A)
B = map(x -> uconvert(unit(eltype(B)), x), B)
return Quantity.(ustrip(A)\ustrip(B), unit(eltype(B))/unit(eltype(A)))
end
end
```
---
### Author:  [@Dan](https://discourse.julialang.org/u/Dan)
#### Post date: [December 28, 2022, 12:42am UTC](https://discourse.julialang.org/t/is-there-a-operator-for-unitful/92195/7 "2022-12-28T00:42:08Z")
There should be another definition of `\` covering the case when `A` is a non-Unitful matrix and `B` is Unitful. Should be pretty similar to the one already defined.