- #1

math8

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For the forward direction, I was thinking that if T and P are projections that have the same diagonal form, their matrices of transformation are similar.

I think I need to use the formula

dimV= dim ker(T)+ dim Im(T) Knowing that dim Im(T)= rank of the matrix of transformation of T and dim ker(T)= n-dim Im(T)

So the result follows.

But I am not sure about the backward direction.