How to rewrite a tensor as a matrix

Question

I put
{TensorProduct[{1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}]}/Sqrt[2]//MatrixForm
and I got
$$
left(
begin{array}{cc}
 left(
begin{array}{cc}
 left(
begin{array}{cc}
 0 & 0 \
 0 & 0 \
end{array}
right) & left(
begin{array}{cc}
 0 & 0 \
 0 & 0 \
end{array}
right) \
 left(
begin{array}{cc}
 0 & 0 \
 0 & 0 \
end{array}
right) & left(
begin{array}{cc}
 0 & 0 \
 0 & frac{1}{sqrt{2}} \
end{array}
right) \
end{array}
right) & left(
begin{array}{cc}
 left(
begin{array}{cc}
 0 & 0 \
 0 & 0 \
end{array}
right) & left(
begin{array}{cc}
 0 & 0 \
 0 & 0 \
end{array}
right) \
 left(
begin{array}{cc}
 0 & 0 \
 0 & 0 \
end{array}
right) & left(
begin{array}{cc}
 0 & 0 \
 0 & 0 \
end{array}
right) \
end{array}
right) \
end{array}
right)
$$
as a result.
I now would like to rewrite this as
$$
left(
begin{array}{cc}
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\
0 & 0 & 0 & frac{1}{sqrt{2}} & 0 & 0 & 0 & 0
end{array}
right)
$$
to calculate eigenvalues of this matrix above.
Could you tell me how?

Suba Thomas · Answer

mat = {TensorProduct[{1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}]/Sqrt[2]};

FixedPoint[ArrayFlatten, mat] // MatrixForm

$left(
begin{array}{cccccccc}
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
 0 & 0 & 0 & frac{1}{sqrt{2}} & 0 & 0 & 0 & 0 \
end{array}
right)$

OkkesDulgerci · Answer

mat = {TensorProduct[{1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}]/ Sqrt[2]};

ArrayFlatten[ArrayFlatten /@ mat] // MatrixForm

$left(
begin{array}{cccccccc}
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \
 0 & 0 & 0 & frac{1}{sqrt{2}} & 0 & 0 & 0 & 0 \
end{array}
right)$

Roman · Answer

X = {TensorProduct[{1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}]/Sqrt[2]};

Flatten[X, {{1, 3, 5}, {2, 4, 6}}]

(*    {{0, 0, 0, 0, 0, 0, 0, 0},
       {0, 0, 0, 0, 0, 0, 0, 0},
       {0, 0, 0, 0, 0, 0, 0, 0},
       {0, 0, 0, 1/Sqrt[2], 0, 0, 0, 0}}    *)

Nasser · Answer

Another option
(m = {TensorProduct[{1, 0}, {0, 1}, {0, 1}, {0, 1}, {0, 1}]}/Sqrt[2]) // MatrixForm

And now
m1 = ArrayFlatten[m[[1, 1]], 2]
m2 = ArrayFlatten[m[[1, 2]], 2]
Join[m1, m2, 2] // MatrixForm

How to rewrite a tensor as a matrix

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