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| Guest |
 Posted: Sat Oct 21, 2006 9:00 am |
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Hi,
I have a lemma,
V c R^n is a linear subspace. Denote by <A|V> the smallest A-invariant
subspace whihc contains V
[A-invariant subspace W, w element W => A_w element of W]
Then <A|V> = V + AV + .... + A^n-1 V
Having a bit of a brain freeze at the moment, but im trying to
visualise this by an example of when A does not equal V, any example
would be great
Thank you |
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| Tonico |
| Posted: Sat Oct 21, 2006 9:26 am |
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Guest
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figurt@hotmail.com wrote:
[quote:6bba5e8d6b]Hi,
I have a lemma,
V c R^n is a linear subspace. Denote by <A|V> the smallest A-invariant
subspace whihc contains V
[A-invariant subspace W, w element W => A_w element of W]
Then <A|V> = V + AV + .... + A^n-1 V
Having a bit of a brain freeze at the moment, but im trying to
visualise this by an example of when A does not equal V, any example
would be great
Thank you
***************************************[/quote:6bba5e8d6b]
Hi:
Take R^3, A(x,y,z):= (-x,-y,z) and V:=<(1,1,0)>. Well, then <A|V> = V
since V itself is A-invariant.
Now if the above is right, then "A does not equal V" doesn't make much
sense: V is a L.S., A is a lin. transf...
You could take V = <(1,0,0)> in the above example, and then <A|V> woild
be, I think, the above V...
Regards
Tonio |
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