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Timeline for Eigenvalues of this matrix

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Sep 28, 2014 at 23:55 history edited BaoLing CC BY-SA 3.0
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Sep 28, 2014 at 15:58 comment added BaoLing well, if I plug in $T(1)$, then $k=0$, so $x^{-1}$ and $x^{-2}$ vanish. And if I plug in $T(x)$, then $k=1$, so $x^{-1}$ vanishes. and yes, I have checked a few cases, although not all the ones that you suggested, cause the equations become so nasty for $m \ge 4$, that you cannot tell in general, if the eigenvalues are real for all $w$ or not.
Sep 28, 2014 at 15:38 comment added Joonas Ilmavirta Have you checked any cases by hand (or computer)? A numerical check for $2\leq m\leq 10$ will give you a good hint. Also, do you mean $x^{-1}=x^{-2}=0$ in your formula?
Sep 28, 2014 at 15:02 history edited BaoLing CC BY-SA 3.0
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Sep 28, 2014 at 14:55 review First posts
Sep 28, 2014 at 15:39
Sep 28, 2014 at 14:53 history asked BaoLing CC BY-SA 3.0