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seen Sep 16 at 22:32

Oct
14
awarded  Popular Question
Jul
2
awarded  Curious
May
11
awarded  Yearling
Apr
16
comment Uniqueness of Singular Values
Thanks, I forgotten the possible rectangularness of $U$s...
Apr
16
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!
Apr
16
accepted Uniqueness of Singular Values
Apr
16
comment Uniqueness of Singular Values
Many thanks again.
Apr
16
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 $M$..
Apr
16
comment Uniqueness of Singular Values
Very clear and detailed, thanks. With $\rho(-)$ you are indicating the spectral radus?
Apr
16
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.
Apr
16
asked Uniqueness of Singular Values
Apr
14
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.
Apr
13
accepted Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
Apr
13
comment Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
Perhaps you missed a $\sigma^2$ in $2t\Big|\big<Av_2,Av_1\big>\Big|^2 \leq ||v_2||^2-||Av_2||^2$? I mean, probably $2t\Big|\big<Av_2,Av_1\big>\Big|^2 \leq \mathbf{ \sigma}^2||v_2||^2-||Av_2||^2$. Right? However, awesome proof. You managed to construct it from scratch? Impressive.
Apr
12
revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
edited title
Apr
11
revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
added 41 characters in body
Apr
10
revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
added 137 characters in body
Apr
10
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..
Apr
10
revised Mysterious Proof about Induced Norms (was: Uniqueness of SVD)
added 190 characters in body
Apr
10
asked Mysterious Proof about Induced Norms (was: Uniqueness of SVD)