n! permutation matrices

I need to generate 24 (4!) distict permutation 4x4 matrices. How would I do that?

The first one would need to be the identity matrix =

[1 0 0 0

0 1 0 0

0 0 1 0

0 0 0 1]

Each other would be variations of the identity matrix having different order of rows of the identity matrix. There would be exactly 24 (4!) different possible distict variations of the identity matrix, counting the identity matrix.

Answer 1

[JESUS DAVID ARIZA ROYETH]

identity=eye(4);
total=perms(1:4);
for k=1:24
matrixperm=identity(total(k,:),:)
end

[Daniel Brower]

How would I put each matrixperm in a cell or array?

Answer 2

[Fabio Freschi]

Is this what you wish?

% identity matrix
A = eye(4);
% permuatations
idx = perms(1:4);
% all matrices in a cell array
B = arrayfun(@(i)A(idx(i,:),:),1:24,'UniformOutput',false)

[Daniel Brower]

Is there a way to change the cells in B into matrices? I am not familiar with using cells.

Answer 3

[Stephen23]

A purely numeric solution without loops:

>> I = eye(4);
>> M = reshape(I(:,flipud(perms(1:4)).'),4,4,24)
M =
ans(:,:,1) =
   1   0   0   0
   0   1   0   0
   0   0   1   0
   0   0   0   1
ans(:,:,2) =
   1   0   0   0
   0   1   0   0
   0   0   0   1
   0   0   1   0
ans(:,:,3) =
   1   0   0   0
   0   0   1   0
   0   1   0   0
   0   0   0   1
ans(:,:,4) =
   1   0   0   0
   0   0   0   1
   0   1   0   0
   0   0   1   0
ans(:,:,5) =
   1   0   0   0
   0   0   1   0
   0   0   0   1
   0   1   0   0
ans(:,:,6) =
   1   0   0   0
   0   0   0   1
   0   0   1   0
   0   1   0   0
... more here
ans(:,:,21) =
   0   0   1   0
   0   1   0   0
   0   0   0   1
   1   0   0   0
ans(:,:,22) =
   0   0   0   1
   0   1   0   0
   0   0   1   0
   1   0   0   0
ans(:,:,23) =
   0   0   1   0
   0   0   0   1
   0   1   0   0
   1   0   0   0
ans(:,:,24) =
   0   0   0   1
   0   0   1   0
   0   1   0   0
   1   0   0   0

Answer 4

[Bandar]

You may consider creating multidemintional matrix as follows:

I=eye(4);
pr=perms(1:4);
A=zeros(4,4,24);
for i=1:24
A(:,:,i) = I(pr(i,:),:);
end
A