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

[Bulutoglu, Dursun A Civ USAF AETC AFIT/ENC]

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.