# How to extract the upper/lower triangular matrix values except the diagonal?
**URL:** https://discourse.julialang.org/t/how-to-extract-the-upper-lower-triangular-matrix-values-except-the-diagonal/112974
**Category:** Statistics
**Tags:** matrix
**Created:** [April 15, 2024, 5:49pm UTC](https://discourse.julialang.org/t/how-to-extract-the-upper-lower-triangular-matrix-values-except-the-diagonal/112974 "2024-04-15T17:49:57Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@Shayan](https://discourse.julialang.org/u/Shayan)
#### Post date: [April 15, 2024, 5:49pm UTC](https://discourse.julialang.org/t/how-to-extract-the-upper-lower-triangular-matrix-values-except-the-diagonal/112974/1 "2024-04-15T17:49:57Z")
Consider the following matrix:
```julia
julia> c = rand(2, 2)
2×2 Matrix{Float64}:
0.0443768 0.515352
0.531426 0.967584
```
Expected output:
```julia
1-element Vector{Float64}:
0.531426
```
I can do:
```julia
julia> using LinearAlgebra: LowerTriangular
julia> LowerTriangular(c)
2×2 LowerTriangular{Float64, Matrix{Float64}}:
0.0443768 ⋅
0.531426 0.967584
```
Collecting the previous lower triangular includes the diagonal of the matrix too. I want to omit the diagonal. How to do it?
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [April 15, 2024, 5:53pm UTC](https://discourse.julialang.org/t/how-to-extract-the-upper-lower-triangular-matrix-values-except-the-diagonal/112974/2 "2024-04-15T17:53:37Z")
> [@Shayan](#):
>
> Collecting the previous lower triangular includes the diagonal of the matrix too. I want to omit the diagonal.
You can use the [`tril` function](https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#LinearAlgebra.tril):
```julia
julia> c = rand(4,4)
4×4 Matrix{Float64}:
0.508891 0.659778 0.639252 0.569137
0.212345 0.834971 0.233612 0.564073
0.812287 0.760213 0.224285 0.466787
0.872574 0.516204 0.701075 0.359622
julia> LowerTriangular(tril(c, -1))
4×4 LowerTriangular{Float64, Matrix{Float64}}:
0.0 ⋅ ⋅ ⋅
0.212345 0.0 ⋅ ⋅
0.812287 0.760213 0.0 ⋅
0.872574 0.516204 0.701075 0.0
```
It’s not clear how useful the `LowerTriangular` type is here, however, rather than simply `tril(c, -1)` stored as a `Matrix`. The main utility of the `LowerTriangular` type is to support fast methods for solving Lx =b lower-triangular systems, but with a zero diagonal the problem is singular so those methods aren’t applicable.
(Another application of `LowerTriangular` is to have an in-place lower-triangular view of a matrix where you are storing something else in the upper triangle, as sometimes happens with in-place matrix factorizations, but that’s not the case if you use `tril`.)
---
### Author:  [@Shayan](https://discourse.julialang.org/u/Shayan)
#### Post date: [April 15, 2024, 5:55pm UTC](https://discourse.julialang.org/t/how-to-extract-the-upper-lower-triangular-matrix-values-except-the-diagonal/112974/3 "2024-04-15T17:55:25Z")
> [@stevengj](#):
>
> `LowerTriangular(tril(c, -1))`
Isn’t `tril(c, -1)` enough?
> [@stevengj](#):
>
> It’s not clear how useful the `LowerTriangular` type is here, however, rather than simply `tril(c, -1)` stored as a `Matrix`. The main utility of the `LowerTriangular` type is to support fast methods for solving Lx =bLx=bLx =b lower-triangular systems, but with a zero diagonal the problem is singular so those methods aren’t applicable.
Thank you so much!
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [April 15, 2024, 5:56pm UTC](https://discourse.julialang.org/t/how-to-extract-the-upper-lower-triangular-matrix-values-except-the-diagonal/112974/4 "2024-04-15T17:56:15Z")
> [@Shayan](#):
>
> Isn’t `tril(c, -1)` enough?
Yes, depends on what matrix type you want to use. See also the comments at the bottom of my revised post (I was editing it while you responded).
---
### Author:  [@Dan](https://discourse.julialang.org/u/Dan)
#### Post date: [April 15, 2024, 6:07pm UTC](https://discourse.julialang.org/t/how-to-extract-the-upper-lower-triangular-matrix-values-except-the-diagonal/112974/5 "2024-04-15T18:07:52Z")
If you wanted the vector of entries, maybe this will do:
```julia
julia> A = rand(3,3)
3×3 Matrix{Float64}:
0.212689 0.222497 0.34268
0.376084 0.004906 0.706805
0.395929 0.334694 0.883166
julia> [v for (k,v) in pairs(A) if k[1]>k[2]]
3-element Vector{Float64}:
0.37608410776838963
0.3959294893831178
0.33469399665884414
```