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

[Sandeep Murthy]

Hello,

I only have general comments, since I am still discovering the 
possibilities of GAP, with respect to answering related questions
of interest to myself.

If V is your f.d. (?) vector space (over some field K), and W < V is
some fixed nontrivial subspace, and P is the projection operator
of V onto W, and f : V --> V is some endomorphism, then it is known
that W is invariant under f, with image f(W) = W' \subseteq W, if and
only if

	(fP)(V) = (PfP)(V) = W' \subseteq W.

If Inv_V(W) is your algebra of all endomorphisms f : V --> V that 
leave W fixed, and End(V) is the algebra containing Inv_V(W)
as a subalgebra, then as a set

     Inv_V(W) = { f \in End(V) | (PfP)(V) = (fP)(V) }.

This is an infinite set, but is the set of elements of an f.d. space, so on GAP, 
I guess you would construct it by specifying a basis.

Sincerely, Sandeep.

On 19 Nov 2011, at 22:49, 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.
> 
> Dursun.
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