# How to convert a itensor to a matrix

**URL:** <https://itensor.discourse.group/t/how-to-convert-a-itensor-to-a-matrix/462>\
**Category:** ITensor Julia Questions\
**Created:** [October 13, 2022, 7:45am UTC](https://itensor.discourse.group/t/how-to-convert-a-itensor-to-a-matrix/462 "2022-10-13T07:45:07Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![phyjswang](https://avatars.discourse-cdn.com/v4/letter/p/f9ae1b/32.png) [@phyjswang](https://itensor.discourse.group/u/phyjswang)\
**Post date:** [October 13, 2022, 7:45am UTC](https://itensor.discourse.group/t/how-to-convert-a-itensor-to-a-matrix/462/1 "2022-10-13T07:45:07Z")

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Hi, Miles and Matt

The MPO Hamiltonian itensor is generated as follows

```julia
using ITensors

let
    N = 2
    sites = siteinds("S=1/2",N;conserve_qns = true)

    ampo = OpSum()
    for j=1:N-1
        ampo += "Sz",j,"Sz",j+1
        ampo += 0.5,"S+",j,"S-",j+1
        ampo += 0.5,"S-",j,"S+",j+1
    end

    H = MPO(ampo,sites)

    Hitensor = ITensor(1.)
    for i = 1:N
        Hitensor *= H[i]
    end
end

```

Basically, all bond indices are constructed, and the resulting `Hitensor` only has physical indices. I am trying to get its matrix form using `matrix(Hitensor)`, but it returns the following error message:

```auto
ERROR: DimensionMismatch: 
Stacktrace:
 [1] matrix(T::ITensor)
   @ ITensors ~/.julia/packages/ITensors/5CAqA/src/itensor.jl:2818
 [2] top-level scope
   @ REPL[64]:1

```

I’ve checked this [doc](https://itensor.github.io/ITensors.jl/stable/ITensorType.html#NDTensors.matrix-Tuple%7BITensor,%20Vararg%7BAny%7D%7D), but still can not find the correct method.

Can you give me an example to obtain it?

By the way, is this matrix still a sparse matrix? Because my purpose of doing all this is to perform ED calculation for benchmark. I know these is a function `eigen` to do this. But it turns out to be inefficient for obtaining all eigenvalues without eigenvectors (correct me if I am wrong) when the system size becomes relatively large. So here I simply try to firstly generate a sparse matrix then resort to other packages or even using `eig` from `matlab`.

Best,  
Junsen

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**Author:** ![sandipanmanna](https://avatars.discourse-cdn.com/v4/letter/s/ee7513/32.png) [@sandipanmanna](https://itensor.discourse.group/u/sandipanmanna)\
**Post date:** [October 13, 2022, 1:25pm UTC](https://itensor.discourse.group/t/how-to-convert-a-itensor-to-a-matrix/462/2 "2022-10-13T13:25:12Z")

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You need to provide the indices for conversion to Matrix(only for 2-dimensional ITensor)/array.Note,the order of indices are important as it may change the representation of the final matrix you get.  
You can try the following once.

```auto
A=Array(Hitensor,sites[1]',sites[2]',sites[1],sites[2])
println(reshape(A,4,4))

```

The output is

```auto
4×4 Matrix{Float64}:
 0.25 0.0 0.0 0.0
 0.0 -0.25 0.5 0.0
 0.0 0.5 -0.25 0.0
 0.0 0.0 0.0 0.25

```

The following link may be helpful.  
[https://docs.juliahub.com/ITensors/P3pqL/0.2.3/ITensorType.html#Convert-to-Array](https://docs.juliahub.com/ITensors/P3pqL/0.2.3/ITensorType.html#Convert-to-Array)

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<div class="post-metadata">

**Author:** ![phyjswang](https://avatars.discourse-cdn.com/v4/letter/p/f9ae1b/32.png) [@phyjswang](https://itensor.discourse.group/u/phyjswang)\
**Post date:** [October 13, 2022, 1:42pm UTC](https://itensor.discourse.group/t/how-to-convert-a-itensor-to-a-matrix/462/3 "2022-10-13T13:42:26Z")

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Thank you for the help. It works now 🙂  
Although I am still wondering how to make the function `matrix` working…

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<div class="post-metadata">

**Author:** ![sandipanmanna](https://avatars.discourse-cdn.com/v4/letter/s/ee7513/32.png) [@sandipanmanna](https://itensor.discourse.group/u/sandipanmanna)\
**Post date:** [October 13, 2022, 2:20pm UTC](https://itensor.discourse.group/t/how-to-convert-a-itensor-to-a-matrix/462/4 "2022-10-13T14:20:30Z")

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As far I am aware, `matrix` is for ITensor with 2 indices . In your case,it has 4 indices. `matrix` doesn’t need indices for conversion as it orders row/column as per ITensor’s internal storage layout.On the other hand, `Matrix` does need you to specify the indices.  
e.g.

```auto
ind = Index(3, "i")
randT = randomITensor(ind', dag(ind)) # two indices
M = matrix(randT)
#The above command is equivalent to the one below.
#M = Matrix(randT, ind', ind)

```

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<div class="post-metadata">

**Author:** ![phyjswang](https://avatars.discourse-cdn.com/v4/letter/p/f9ae1b/32.png) [@phyjswang](https://itensor.discourse.group/u/phyjswang)\
**Post date:** [October 13, 2022, 2:23pm UTC](https://itensor.discourse.group/t/how-to-convert-a-itensor-to-a-matrix/462/5 "2022-10-13T14:23:09Z")

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Thank you very much, everything is clear now 😀