Working with a set of matrices

I want to generate a finite matrix group by starting with the S ={identity} and multiplying by some generators until S no longer grows in size.

Is there an efficient way to deal with a "set" like this, without manualling checking for duplicates? For example, it seems awkward if you use cell arrays to store the elements of S.

[Matt J]

For example, it seems awkward if you use cell arrays to store the elements of S.

Why?

[Lorcan O'Connor]

Well say I multiply everything in the cell array by a matrix and only want to take the new elements, how do I efficiently take a “set Union” (or even check if a matrix is in the array), without just looping and checking everything?

Answer 1

[Matt J]

I'm not sure I will fully understand the task without seeing an example. However, if S is organized as an MxNxP array,

[M,N]=deal(3,3);
S=cat(3,eye(M,N), randi(5,M,N), eye(M,N) )

S = 
S(:,:,1) =

     1     0     0
     0     1     0
     0     0     1


S(:,:,2) =

     4     5     4
     2     1     3
     1     5     2


S(:,:,3) =

     1     0     0
     0     1     0
     0     0     1

then you can get rid of duplicate slices with

s=reshape(S,[],size(S,3));
S=reshape( unique(s.','rows').', M,N,[])

S = 
S(:,:,1) =

     1     0     0
     0     1     0
     0     0     1


S(:,:,2) =

     4     5     4
     2     1     3
     1     5     2

If S contains non-integer matrices, you will probably need to use uniquetol() instead of unique().

[Lorcan O'Connor]

Thanks a lot that's exactly what I needed