Let $U$ be orthogonal. How can I prove that $||UA||_2=||A||_2$?
I know that $||UA||_2\le||U||_2||A||_2$ and I also know that as $U$ is orthogonal, $U^{-1}=U^T$. But I don't know what else to do...
2026-03-27 16:55:24.1774630524
Let $U$ be orthogonal. How can I prove that $||UA||_2=||A||_2$?
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Hint: since $U^TU=I$, $(UA)^TUA=A^TU^TUA=\cdots$