86.6 DecomposedMat

DecomposedMat( mat )

finds if the square matrix mat admits a block decomposition. Define a graph G with vertices [1..Length(mat)] and with an edge between i and j if either mat[i][j] or mat[j][i] is non-zero. DecomposedMat return a list of lists l such that l[1],l[2], etc.. are the vertices in each connected component of G. In other words, the matrices mat{l[1]}{l[1]},mat{l[2]}{l[2]}, etc... are blocks of the matrix mat.

    gap> m := [ [  0,  0,  0,  1 ],
    >           [  0,  0,  1,  0 ],
    >           [  0,  1,  0,  0 ],
    >           [  1,  0,  0,  0 ] ];;
    gap> DecomposedMat( m );
    [ [ 1, 4 ], [ 2, 3 ] ]
    gap> PrintArray( m{[ 1, 4 ]}{[ 1, 4 ]});
    [ [  0,  1 ],
      [  1,  0 ] ] 

Previous Up Top Next
Index