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 Oct14 awarded Popular Question Jul2 awarded Curious May11 awarded Yearling Apr16 comment Uniqueness of Singular Values Thanks, I forgotten the possible rectangularness of $U$s... Apr16 comment Uniqueness of Singular Values Ok, so we would have used $\hat{U}=M^T U M$, IF we did select the same basis for the domain, but here we are selecting two different bases on the very purpose. Thank you again, perfectly clear! Apr16 accepted Uniqueness of Singular Values Apr16 comment Uniqueness of Singular Values Many thanks again. Apr16 comment Uniqueness of Singular Values And why $\hat{U}=UM$ and not $\hat{U}=M^T UM$? After all, $\hat{U}$ and $U$ should be similar via the orthogonal change of basis operated by $M$.. Apr16 comment Uniqueness of Singular Values Very clear and detailed, thanks. With $\rho(-)$ you are indicating the spectral radus? Apr16 comment Uniqueness of Singular Values Thanks. I'm in a struggle about what answer to accept. Pavel gave a bit more detailed explanation, but you answered first. Apr16 asked Uniqueness of Singular Values Apr14 comment Mysterious Proof about Induced Norms (was: Uniqueness of SVD) @Markus: I suppose what Ewan Delanoy exposed in his post is essentially taken for granted by Trefethen. Probably a "give details of the proof" approach. Or at least I hope so. Apr13 accepted Mysterious Proof about Induced Norms (was: Uniqueness of SVD) Apr13 comment Mysterious Proof about Induced Norms (was: Uniqueness of SVD) Perhaps you missed a $\sigma^2$ in $2t\Big|\big\Big|^2 \leq ||v_2||^2-||Av_2||^2$? I mean, probably $2t\Big|\big\Big|^2 \leq \mathbf{ \sigma}^2||v_2||^2-||Av_2||^2$. Right? However, awesome proof. You managed to construct it from scratch? Impressive. Apr12 revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD) edited title Apr11 revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD) added 41 characters in body Apr10 revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD) added 137 characters in body Apr10 comment Mysterious Proof about Induced Norms (was: Uniqueness of SVD) Same considerations struck my mind, but like you I tend to exclude the possibility of a such big mistake by a guy that teaches at Oxford.. Apr10 revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD) added 190 characters in body Apr10 asked Mysterious Proof about Induced Norms (was: Uniqueness of SVD)