Re: Direct Sums

Robert Low wrote: 
SportsNut wrote:

Or do I NEED the fact that R(T)*intersection*N(T)={0}?
NOTES: R(T)= range of T
N(T)= null space of T
V= finite dimensional vector space
T:V->V is linear

[stuff deleted]
 so your 'fact' is actually
untrue.
This suggests that you have the
question incorrect.


Or just possibly that I misread your post.
Oh well.

I thought you were trying to prove that
V=R(T) direct sum N(T) in general.

If in fact you are trying to prove that
whenever V=R(T)+N(T) then it is also true
that V=R(T) direct sum N(T), then yes,
you have to prove that R(T) n N(T)
contains only the zero vector.
.

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