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Results tagged with eigenvalues
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user 10265
eigenvalues of matrices or operators
5
votes
Accepted
Lower bounds on matrix eigenvalues
The product of the eigenvalues of $A^t A$ does not depend on $x$ (it is equal to $det(A)^2=\alpha^4$), whereas their sum goes to $\infty$ (it is $Tr(A^tA)=2\alpha^2+x^2$). … Hence one the the eigenvalues goes to $\infty$, and the other to $0$. …
- 9,486
3
votes
Accepted
Tight upper bound on a ratio involving symmetric PSD matrices and Kronecker products
There is no upper for $m$ that is independent of $d$ and $T$. In fact, for a fixed $d$, the best upper bound that works for all $T$ is of order $\sqrt{d}$, and this is already tight for $T=d$.
The bou …
- 9,486
2
votes
eigenvalues of matrices (with positive entries)
This is clearly a mistake, for example the singular values of the matrix $\begin{pmatrix} 1 & 1\\1&1\end{pmatrix}$ are $(2,0)$ and not $(\sqrt 2,\sqrt 2)$.
But it is harmless here, as the only thing t …
- 9,486