Create a block diagonal matrix with different sizes of blocks in GAP

block matricescomputational-algebragap

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Problem: I want to create a block diagonal matrix with different size of blocks in GAP, for example with a block $1\times 1$ and a block $2\times 2$. I read the manual of GAP and I found the command "BlockMatrix" but I don't understand if it is possible to create such a matrix it with different sizes of blocks.

Thanks in advance!

Best Answer

As long as the blocks are diagonal, you can use DirectSumMat with the matrices to be placed along the diagonal as arguments:

gap> m1:=[[1,2],[3,4]];;
gap> m2:=[[1,2,3],[4,5,6],[7,8,9]];;
gap> DirectSumMat(m1,m2);
[ [ 1, 2, 0, 0, 0 ], [ 3, 4, 0, 0, 0 ], [ 0, 0, 1, 2, 3 ], [ 0, 0, 4, 5, 6 ],
  [ 0, 0, 7, 8, 9 ] ]

If the blocks are not along the diagonal, you would have to build the matrix yourself.

(BlockMatrix is a special representation where blocks must have the same dimension, used mainly for representing induced representations)

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