Nilpotent matrix corresponding to a partition via gap

Question

is there a command/quick way in GAP, that gives me the corresponding nilpotent Matrix in jordan normalform(as an element of the matrix algebra MatAlgebra(GF(a),b)) when I enter a Partition and a field? So ([2],GF(3)) should enter the matrix [[0*Z(3),Z(3)^0],[0*Z(3),0*Z(3)]].

I'm not entirely sure how you a partition will give you a matrix, and how to interpret [2] as corresponding to the matrix you give. Can you give a bit more explanation of how the map works, then it probably won't be hard to give a brief function. — ahulpke, May 28 '16 at 15:44
I mean the nilpotent Matrix in jordan normalform having Jordan-blocks of size $a_i$ when $a_1,a_2,...,a_r$ is the partition. — Mare, May 28 '16 at 17:38

score 2 · Accepted Answer · answered May 29 '16 at 16:31

With the specification of a partition and fixed eigenvalue 0 it is in the end less work to write a specialized function than to try to paste it together from existing bits:

MareMat:=function(part,f)
local m,o,c,j;
  m:=NullMat(Sum(part),Sum(part),f);
  o:=1;
  for c in part do
    for j in [1..c-1] do
      m[o][o+1]:=One(f);
      o:=o+1;
    od;
    o:=o+1;
  od;
  return m;
end;

The function simply takes a zero matrix and adds appropriate 1's off the diagonal. The variable $o$ is a counter through the rows of the matrix.

Nilpotent matrix corresponding to a partition via gap

1 Answers1