Hello,

I would like help in:

Assume T and U are in L(V,V ) and that V = N(T)+N(U). Prove that TU = T0 . (T0 is the zero linear transformation)

Thank you

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- November 5th 2009, 10:04 AMNonaProve that TU = T0
Hello,

I would like help in:

Assume T and U are in L(V,V ) and that V = N(T)+N(U). Prove that TU = T0 . (T0 is the zero linear transformation)

Thank you

- November 5th 2009, 10:44 AMtonio

Let's see if I succeed in decoding the above: T,U are linear operators and N(T), N(U) are the corresponding null spaces, or kernel, of these operators.

So, if then .

Assuming I guessed correctly your symbols, the claim is false: as example take ,

It's easy to check that , but , as you can easily check.

If by the above symbols you meant something else then the above is worthless (perhaps the above's worthless EVEN if I guessed correctly your symbols).

Tonio - November 5th 2009, 11:11 AMNona
Yes, you guessed write. And this is the question that I have to prove that TU=T_0.

I wonder if Prof. quotation is to prove TU not equal T_0. maybe typo

Thank you very much