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Jan 11, 2023 at 13:07 vote accept Raz Kupferman
Jul 5, 2022 at 10:05 history edited MyShepherd CC BY-SA 4.0
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Jul 5, 2022 at 9:59 history edited MyShepherd CC BY-SA 4.0
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Jul 5, 2022 at 4:37 history edited MyShepherd CC BY-SA 4.0
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Jul 5, 2022 at 4:35 comment added MyShepherd Thanks. You are right, but I was under the impression that @Raz Kupferman meant that $\|{B}\|<2$, since as your example shows otherwise the eigenvalues may be purely imaginary. In any event, I corrected the inequality by $P(\xi)\geq c|\xi|^{2}I$ for some constant $c>0$, this is all that is needed, I think.
Jul 4, 2022 at 19:21 comment added Iosif Pinelis Concerning the inequality $|\xi|^{2}I\le P(\xi)$: If e.g. $\lambda=\xi_\mu=1$, $A=C=I$, and $B=2I$, then the inequality becomes $2I\le0I$, which is not true.
Jul 4, 2022 at 18:14 history edited MyShepherd CC BY-SA 4.0
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Jul 4, 2022 at 17:42 history edited MyShepherd CC BY-SA 4.0
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Jul 4, 2022 at 17:36 history edited MyShepherd CC BY-SA 4.0
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Jul 4, 2022 at 17:22 history edited MyShepherd CC BY-SA 4.0
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Jul 4, 2022 at 17:16 history edited MyShepherd CC BY-SA 4.0
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Jul 4, 2022 at 17:10 history answered MyShepherd CC BY-SA 4.0