Let $V$ be an inner product space of finite dimension, and $T:V \to V$ a linear map. Prove that $Im(T)=Im(TT^*)$.
Proving that $Im(TT^*) \subseteq Im(T)$ was not a problem, but I'm having trouble proving the other direction. Ideas?
2026-04-28 19:01:15.1777402875
Proving that $Im(T) = Im(TT^*)$ (hermitian adjoint)
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Hint: $im(T^*)=\ker(T)^\perp$.