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## N(T) \bigoplus R(T) = V ## where ##V## is the source of the linear map ##T:V → V## ?

BiP

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- Thread starter Bipolarity
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- #1

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## N(T) \bigoplus R(T) = V ## where ##V## is the source of the linear map ##T:V → V## ?

BiP

- #2

Office_Shredder

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T(x,y) = (y,0).

This is a linear map from R

- #3

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T(x,y) = (y,0).

This is a linear map from R^{2}to R^{2}. The null space is (x,0) for x in R and the range is (x,0) for x in R, so N(T)+R(T) is just the x-axis

I see. Suppose that you knew the statement to be true. Then could you conclude that T is invertible?

BiP

- #4

Office_Shredder

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It's not hard to construct a projection in two dimensions which is a counterexample to that claim

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