[GAP Forum] similar matrices

[Burkhard Höfling]

On 13.03.2008, at 07:18, Vahid Dabbaghian wrote:

>
> Dear GAP forum,
>
> Suppose A and B are similar and invertible matrices on C. Does  
> anybody know
> a function or a program in GAP to compute an invertible matrix P  
> such that
> P^{-1}AP=B ?

A straightforward way is to write AP = PB and to solve the system of  
linear equations in the entries of P. For reasonalby samll matrices,  
this works well.

If your matrices are over the complex numbers, then you can also  
conjugate both into Jordan normal form and find a suitable  
permutation matrix to conjugate one Jordan normal form into the other.

A similar approach might work for matrices over finite fields. In my  
package IRREDSOL, I have used such an approach for computing  
conjugating matrices of irreducible matrix groups.

Cheers,

Burkhard.