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Find the Spectral Radius of $A=$ $\mbox{} \left[ \begin{array}{cc} 1 & 0 & 0 & 0 \\ 0 & 0 & c & 0 \\ 0 & -c & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right]$

After going through the motions, I got that the $-x^{3}-c^{2}x=0$ $\Rightarrow$ $-x(x^{2}+c^{2})$

Now C is supposed to be in $\mathbb{R}$ while $A \in \mathbb{C}$

When I use the quadratic formula, I get that 2iC=0, and by the definition the spectral radius is the largest absolute value of the eigenvalues.

So what am I to make of the results of the quadratic formula? On the right path?

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    Care to explain how you get $2iC = 0$ rather than $x = something$ from the quadratic formula?2012-09-26
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    Okay, totally understand mistake. Thank you.2012-09-26
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    Then would $i c$ be the largest possible eigenvalue?2012-09-26

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