# Inverse of a triangular matrix
**URL:** https://discourse.julialang.org/t/inverse-of-a-triangular-matrix/49620
**Category:** Performance
**Tags:** linearalgebra
**Created:** [November 5, 2020, 9:37am UTC](https://discourse.julialang.org/t/inverse-of-a-triangular-matrix/49620 "2020-11-05T09:37:49Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@stla](https://discourse.julialang.org/u/stla)
#### Post date: [November 5, 2020, 9:37am UTC](https://discourse.julialang.org/t/inverse-of-a-triangular-matrix/49620/1 "2020-11-05T09:37:49Z")
Hello,
Is there an optimized way to inverse a triangular matrix? I searched with Google, no luck.
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### Author:  [@moeddel](https://discourse.julialang.org/u/moeddel)
#### Post date: [November 5, 2020, 10:18am UTC](https://discourse.julialang.org/t/inverse-of-a-triangular-matrix/49620/2 "2020-11-05T10:18:05Z")
julia does provide specialized types `UpperTriangular`, `UnitUpperTriangular`, `LowerTriangular`, and `UnitLowerTriangular`. In the documentation it is stated that there are optimized functions for `inv` and `det`.
[https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LAPACK-functions](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LAPACK-functions)
This is a small example of how this should work:
```julia
using LinearAlgebra
A = [1.0 2.0 3.0; 0.0 5.0 6.0; 0.0 0.0 9.0]
3×3 Array{Float64,2}:
1.0 2.0 3.0
0.0 5.0 6.0
0.0 0.0 9.0
UTA = UpperTriangular(A)
3×3 UpperTriangular{Float64,Array{Float64,2}}:
1.0 2.0 3.0
⋅ 5.0 6.0
⋅ ⋅ 9.0
inv(UTA)
3×3 UpperTriangular{Float64,Array{Float64,2}}:
1.0 -0.4 -0.0666667
⋅ 0.2 -0.133333
⋅ ⋅ 0.111111
```
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### Author:  [@stla](https://discourse.julialang.org/u/stla)
#### Post date: [November 5, 2020, 11:11am UTC](https://discourse.julialang.org/t/inverse-of-a-triangular-matrix/49620/3 "2020-11-05T11:11:46Z")
Ah nice, thanks!