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.
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