Let $\displaystyle \pi:V\to V$ be a linear transformation satisfying $\displaystyle \pi^2=\pi$. Prove that Pi is a projection of V onto the Image of Pi along the ker of Pi.
I have no idea but I am guessing the idempotent property is important.
Let $\displaystyle \pi:V\to V$ be a linear transformation satisfying $\displaystyle \pi^2=\pi$. Prove that Pi is a projection of V onto the Image of Pi along the ker of Pi.
I have no idea but I am guessing the idempotent property is important.