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- Thread starter crypt50
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- Feb 7, 2012

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You need to use the definition of the direct sum $X\oplus Y$. The question tells you which subspaces to use for $X$ and $Y$, so what do you have to check in order to show that the definition of $V = X\oplus Y$ is satisfied?Assume also that S + T = Iv and that S ∘ T = Ov = T ∘ S. Prove that V = X ⊕ Y where

X = range(S) and Y = range(T). I don't understand how to go about it, please help.