How can I prove that $AA^+x=x$ for any vector $x \in range(A)$, where $A$ is a non-zero matrix?
2026-03-27 12:11:42.1774613502
Prove that $AA^+x=x$ for $\forall x \in range(A)$
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Since $x \in range(A)$, $x=Ay$ for some $y$.
$$AA^+x=AA^+Ay=Ay=x$$
since $AA^+A=A.$