[GAP Forum] matrix realization over prime field

[Evgeny Vdovin]

Dear all,

Could you give me an idea, how could I realize the following procedure:

Let A be a n*n matrix over a non-prime field GF(p^k) (say, A in GL(2,4)). I
need to generate matrix B of size nk*nk over GF(p) such that each k*k block
in it is an element in GF(p^k) realized as k*k matrices over GF(p) and the
element corresponds to an element of A.

For example, if
A =
[
   [Z(2^2),0*Z(2^2)],
   [0*Z(2^2),Z(2^2)^(-0)]
]
and
Z(2^2) =
[
  [a,b],
  [c,d]
];
Z(2^2)^(-1)=
[
  [x,y],
  [z,t]
],
then
B=
[
  [a,b,0*Z(2),0*Z(2)],
  [c,d,0*Z(2),0*Z(2)],
  [0*Z(2),0*Z(2),x,y],
  [0*Z(2),0*Z(2),z,t]
].

All the best, Evgeny.

-- 
Evgeny Vdovin
Sobolev Institute of Mathematics
pr-t Acad. Koptyug, 4
630090, Novosibirsk, Russia
Office    +7 383 3297663
Fax       +7 383 3332598