[GAP Forum] Calculating the maximum algebra of linear transformations fixing a non-trivial subspace of a vector space

[Bill Allombert]

On Sat, Nov 19, 2011 at 05:49:06PM -0500, Bulutoglu, Dursun A Civ USAF AETC AFIT/ENC wrote:
> Dear Gap forum,
> Given a vector space V and a non-trivial subspace W
> I was wondering whether it is possible to calculate the maximum 
> algebra of linear transformations under which W is invariant.
> 
> Any theoretical or computational insight will be greatly appreciated.

In the finite dimensional case,

Start with a basis w1...wk of W and complete it to a basis of V
w1...wk,v_{k+1}...v_n.
Let f such that W is invariant by f, then the matrix of f can be written by
block as
(A B)  Where A is kxk dimensional, B is (n-k)xk and C is (n-k)x(n-k)
(0 C)

The set of all such matrices is the algebra you seek (if I understand your question
correctly).

Cheers,
Bill.